1 billion in rupees: Billion to Lakhs Crores Million

If we talk about the Indian currency i.e. Rupees, then 1 billion is equal to 10000 lacs.

1 billion is equal to 10000000000 which is a natural number.

The number 1000000001 comes after 1 billion and the number 999999999 comes before it.

To describe in quantities in Math, the concept of place value is used. Primarily, there are two methods that are used extensively for interpreting the place value of the digits in a particular number.

These two methods are the international number system and the Indian number system.

The positional value of a number is determined by using the place value charts.

Numbers in the general form can be extended with the support of positions.

We start ordering the place value from the right direction to the left direction.

The value of place progresses to tens, hundreds, thousands, and many more starting with the unit location i.e. one’s place.

Continue reading to find out the value of 1 billion dollars in rupees in words and the value of 1 billion in rupees of the Indian number system of place value.

We will also describe to you the position value charge for both the international number system and the Indian number system.

Read More

  1. How much is 1 million
  2. Value of 5 million dollars in Indian rupees

The Place Value Charts for the Indian Number System

The position value sequence in the Indian number system is as follows

  1. Ones – 1
  2. Tens – 10
  3. Hundreds – 100
  4. Thousands – 1000
  5. Ten Thousands – 10000
  6. One Lakh – 100000
  7. Ten Lakhs – 1000000
  8. One Crores – 10000000
  9. Ten Crores – 100000000

The Indian number system is also known as the Hindu-Arabic number system.

You can also use a comma between the zeroes to differentiate between the intervals of this numbering scheme.

Here is a basic rule that you need to follow if you wish to use commas between zeros in the Indian number system – The 1st comma will come after three digits from the right and followed by two digits, then followed by two digits, and after that followed by every two digits.

International Number System’s Place Value Chart

The position value sequence of the digits in the International number system is as follows –

  1. Ones – 1
  2. Tens – 10
  3. Hundreds – 100
  4. Thousands – 1000
  5. Ten Thousands – 10000
  6. Hundred Thousands – 100000
  7. One Million – 1000000
  8. Ten Million  – 10000000
  9. Hundred Million  – 100000000
  10. One Billion – 1000000000
  11. Ten Billion  – 10000000000
  12. Hundred Billion  – 100000000000

What essentially means converting billions to rupees?

The place value of digits is referred to in several ways in the international number system and Indian number system.

The digits in the Indian system have place values such as ones, 10s, hundreds, 1000s, 10000s, lacs, 10 lacs, crores, 10 crores, and the sequence goes on in the following manner.

On the other hand, the digits have position values such as ones, tens, hundreds, thousands, ten thousands, hundred thousands, 1 million, 10 million, 100 million, 1 billion, 10 billion,  100 billion, and the sequence goes on in the same manner in the International Number System.

Here’s a quickie – One billion is equal to one hundred crores in the Indian National Rupees. 

1000000000 Indian Rupees = 1 Billion

It is also equivalent to ten thousand lakhs (or 10000 lakhs) as one lakh holds the value of 100000 Indian Rupees.

Therefore, one billion is equal to one hundred crores (or 100 crores).

How can you use the calculator for the conversion of billion to rupees?

A person can use the following rules for the conversion of billion to rupees –

  1. First of all, you are required to type the desired number of billions in the given input space.
  2. Tap on the ‘Convert’ button to get the conversion value.
  3. The conversion value from billions to rupees will be shown in the output region.

The above-mentioned 3 simple steps are the key for converting your desired billion number value to Indian National Rupees in a matter of few seconds.

Conversion From Billion to Lakhs

If you wish to convert billions to lakhs, then you should multiply the given billion value by 10000 lacs to get the result.

For example, if you want to convert 7 billion to lacs, then you should multiply 7 by 10000 lakhs.

10,000 lacs × 7 is equal to 7 billion.

7 billion = 70,000 lacs.

Therefore, as you can see, 70000 lacs is equal to 7 billion.

If we consider one Dollar is equal to 75 Indian Rupees, then 1 billion dollars in Indian National Rupee is equal to 75000000000.

Conversion From Billion to Crores

If you wish to convert the given billion value to crores in the Indian number system, then you should multiply the given billion value by 100 crores.

For example, you wish to convert 9 billion to crores in the Indian number system, then you should multiply 9 by 100 crores to get the desired result.

If we put it in another way, then you can also think that 9 × 100 crores is equal to 9 billion.

9 billion dollar = 900 crores.

Therefore, 9 billion is equal to nine hundred crores in words.

Likewise, you can convert any given billion value to values in the Indian number system such as crores, lacs, and many more.

How many Zeros in a Billion?

There are a total of 9 zeroes present in 1 billion value.

1 billion is equal to 1000000000.

How many Millions is a Billion?

For all of you who don’t know, 1 million is equal to 1000000.

That is, we can also say that 1000 thousand is equal to 1 million.

1000000000 is equal to 1000 million is equal to 1 billion.

So, the value of 1 billion is equal to 1000 million.

1 billion means

1 billion value can be represented by the letters bn and b. 1 billion is equal to 10000 lacs in the Indian number system.

Therefore, in terms of crores, 1 billion is equal to 100 crores that is 1 billion is equal to 1000000000.

1 billion rupees

Now, first of all, let’s consider that the value of $1 is 75 Indian rupees.

Also, you know that the value of 1 billion is 1000000000 Indian Rupees. Therefore the value of 1 billion dollars in Indian rupees will be 75 × 10000000000 = 75000000000 Indian rupees.

1billion in lakhs

On the basis of the position value chart, the international number system uses billions. Now we are going to find the equivalent of 1 billion in the Indian number system –

1 billion in Indian Rupees is equal to 100000000 Indian rupees.

It can also be represented as –

1 billion is equal to 10000 lacs as all of us know that one lakh is equal to 100000.

Therefore, 10000 lakh Indian Rupees is equal to 1 billion in lacs. We can also say that 1 billion lacs is equal to 10 million lacs.

If you wish to convert 1 billion into crores, then we should bring this to your notice that 1 billion is equal to 100 crores.

This is because one crore is equal to 10000000.

10 billion dollars in rupees

As we have discussed 1 billion, now we will convert the given billion-dollar values in Indian national rupees.

For instance, we have taken the value to be 10 billion dollars.

So, let’s start with the basics first here in this segment. All of us know that the value of 1 billion till now.

It is equal to 1000000000 Indian national rupees, which is also a natural number.

The dollar conversion rate at the moment is around 74.42 Indian national rupee.

But for ease of understanding and calculation, we have taken the value to be 75 Indian National rupees.

So, for this segment and for all over this article, the value of 1 dollar is equal to 75 Indian national rupees as a matter of approximation.

Now, before proceeding to the value of 10 billion dollars in rupees, let’s first calculate the value of 10 billion in rupees.

Have a look at the simple formula written beneath –

10 billion is equal to 10 × 1 billion.

i.e. 10 billion = 10 × 1000000000 = 10000000000 Indian National Rupees.

Since we have got the value of 10  billion, now let’s move on to our next step and calculate the value of 10 billion dollars.

10 billion dollars can be easily calculated by multiplying 10 billion by the value of 1 dollar conversion and exchange rate.

10 billion dollars = 10 billion × 1 Dollar

10 billion dollars = 10000000000 × 75

10 billion dollars = 750000000000 Indian national rupees.

The above-mentioned number is the representation of 10 billion dollars in Indian national rupees in numbers. It is also equal to 75  lac crores Indian rupees.

If we talk about the representation of 10 billion dollars in words, then 10 billion dollars can be written as seventy-five lac crores Indian National rupees.

1 billion is equal to how many crores?

A very frequent and common question related to 1 billion is that how much worth is one billion in crores?

So, in this segment, we are going to answer this very interesting and commonly asked question.

1 billion = 1000000000 Indian national rupees.

Now, if we calculate the total number of crores in the above-mentioned figure then the answer comes as 100 crores as 1 crore is equal to 10000000 Indian National Rupees.

In words, one billion can be written or represented as hundred crores.

Further, if one wants to convert one billion or hundred crores to lacs, the required answer will be ten thousand lacs.

1 billion = 10,000 lacs = 100 crores.

One billion is equivalent to how many million?

As established in the previous segment,

10,000 lacs = 100 crores = 1 billion

Now, to convert one billion into millions or to answer the above question, one first needs to understand the concept of one million.

One million is a term used in the international number system. It is equivalent to ten lakhs in the Indian number system.

Therefore,

1 million = 10 Lakhs Indian National Rupees

From the previous segment,

1 billion = Ten thousand lacs or 10000 lakhs.

Dividing the second billion equation by the first million equation, we get

1 billion = 1000 lacs Indian rupees.

In words, it can be written or represented as thousand lacs Indian National Rupees.

1.1 billion in crores

So, amid converting all the integer value billions to lacs, crores and other place value in the Indian number system, now we will be trying and converting a decimal billion value to crores in the Indian number system.

For this example, we will be taking our value as 1.1 billion.

So, the only thing that you need to understand before proceeding on and solving this question is that you should know the value of 1 billion in number and its equivalent value in the Indian number system.

As we have done numerous examples and questions on this topic till now, we hope that you are aware of the answers to both the above questions.

The answer to the 1st question here is that the value of 1 billion is 1,000,000,000 Indian national rupees in numbers.

If we translate that to crores or lakhs, we get our second answer. It is equivalent to 100 crores (or a hundred crores) Indian rupees in the Indian number system.

So, keeping the above 2 points as notes, let’s start deducing the value of 1.1 billion in Indian National Rupees. 

The value of 1.1 billion can be deduced by multiplying 1.1 by 1 billion.

Therefore,

  1. × 1000000000 (One Billion) = 1.1 Billion

1100000000 = 1.1 Billion

Therefore, 1100000000 Indian rupees is the value of 1.1 billion.

This translates to 110 crores (one hundred and ten crores in words) or 11000 lacs (eleven thousand lakhs Indian rupees).

3 billion in rupees

So, now let’s discuss about 3 billion and convert it into Indian national rupees.

1 Dollar is equal to 75 rupees (Assumption taken for this article).

1 billion is equal to 1000000000 Indian rupees in numbers.

So, calculating 3 billion rupees becomes easy now as you just have to multiply 1 billion by 3.

Therefore, 3 billion = 3 × 1000000000 Indian rupees = 3000000000 Indian rupees.

If we talk about this number, then it is followed by 3000000001 and preceded by 2999999999. All of these are pure, natural numbers.

It can be also written or represented as 300 crores or 30000 lacs.

In words, it can be written as three hundred crores Indian rupees or thirty thousand lacs Indian rupees.

2 billion means

All of us know that 1 billion is equal to 10000000000 which is a natural number.

If we wish to calculate 2 billion by the same order and formula, then 2 billion will be equal to 2 X 1000000000 is equal to2000000000 Indian National Rupees.

Therefore, 2 Billion means 2000000000 Indian rupees which is a natural number.

The natural number 1999999999 comes before 2 billion and the natural number 2000000001 comes after 2 billion.

In numbers, it is written or can be represented as 2 hundred crores or 20000 lacs.

In words, 2 billion is equal to two hundred crores or twenty thousand lacs.

4 billion in rupees

Assumption – $1 is equal to 75 Indian rupees.

1 billion = 1000000000 Indian rupees.

4 billion = 4 × 1 billion (1000000000 Indian rupees) = 4000000000 Indian rupees.

4 billion can also be written or represented as 400 crores or 40000 lacs.

In words, four billion is equal to four hundred crores Indian rupees or forty thousand lacs Indian rupees.

5 billion in crores

Now, as you know till now that we have considered the value of $1 as 75 Indian rupees. Also, you know that the value of 1 billion is 1000000000 Indian Rupees. So, the value of 5 billion is 5000000000 Indian rupees.

Therefore, the value of 5 billion in Indian rupees is 500 crores (in crores) or 50,000 lacs.

In words, the value can be written or represented as five hundred crores Indian rupees or fifty thousand lacs Indian rupees.

5 billion dollars in rupees in words

All of us are now aware that 1 billion rupees are equal to 100000000 Indian rupees.

Also, we hope that till now you are aware that we have considered the value of one dollar is equal to 75 Indian rupees.

Therefore the value of 5 billion is equal to 5 x 100000000 and it will be equal to 500000000 Indian rupees.

Therefore, the value of 5 billion dollars in Indian rupees is equal to 50000000 X 75 = 375000000000 Indian rupees.

In words, it can be written as three lakh seventy-five thousand crores Indian rupees.

7 billion in rupees

Coming to 7 billion in Indian rupees, we will go by the same logic that we have followed in the last few conversions of billions into the Indian national rupee.

First of all, as we have considered in the last few conversions, the value of $1 that we will be taking will be 75 Indian National Rupees.

I hope that till now all of you know that 1 billion is equal to 1000000000 Indian National Rupees.

Thus, the value of 7 billion in the Indian number system will be equal to 7 x 1000000000 Indian National Rupees. This amount is equal to 7000000000 Indian national rupees.

If we wish to represent 7 billion in rupees, then it will be equal to 700 crores or 70000 lacs Indian rupees.

In words, it can be written as seven hundred crores or seventy thousand lacs Indian rupees.

8 billion in rupees

Coming to 8 billion in Indian rupees, we will go by the same logic that we have followed in the last few conversions of billions into the Indian national rupee.

First of all, as we have considered in the last few conversions, the value of $1 that we will be taking will be 75 Indian National Rupees.

I hope that till now all of you know that1 billion is equal to 1000000000 Indian National Rupees.

Thus, the value of 8 billion in the Indian number system will be equal to 8 x 1000000000 Indian National Rupees. This amount is equal to 8000000000 Indian national rupees.

If we wish to represent 8 billion in rupees, then it will be equal to 800 crores or 80000 lacs Indian rupees.

In words, it can be written as eight hundred crores or eighty thousand lacs Indian rupees.

12 billion dollars in rupees

Enough of converting x billion value to Indian national rupee. Now, we will be converting the given billion-dollar value to Indian National Rupees.

For example, in this segment, we will be converting 12 billion dollars into Indian national Rupees and will be representing them in numbers, in words, and in rupees.

Over and over, we have told you in this article that we will be considering the value of $1 equal to 75 Indian national rupees.

Also, you must be knowing till now that the value of 1 billion is equal to 1000000000 Indian National Rupees.

Thus, first, let’s calculate the value of 12 billion in Indian rupees. 12 billion will be equal to 12 x 100000000 Indian rupees.  This sum will amount to 12000000000 Indian rupees.

Now, let’s calculate the value of 12 billion dollars from the 12 billion that we have calculated just above right now.

12 billion dollars = 75 × 12000000000 Indian rupees

12 billion dollars = Rs. 900000000000 = 9 lac crores INR.

In words, the value of 12 billion dollars is equal to nine lakh crores Indian rupees.

How many zeros in 10 billion?

By all means, we hope that you know now that 1 billion is equal to 100000000 Indian rupees.

Therefore, as you can see 1 billion consists of 9 zeroes.

The value of 10 billion is equal to 10 X 1 billion equal to 10 × 1000000000 = 10000000000 Indian National Rupees.

Evidently, 10 billion consists of 10 zeroes.

In rupees, it is equal to 1000 crores or 1 lac lacs Indian National Rupees.

In words, it is equal to thousand crores Indian rupees or one lac lacs Indian national rupees.

What is the value of 5 million dollars in Indian rupees?

How much are 5 million dollars in Indian rupees?

You can calculate easily you must know the value of 5 million and price of a dollar multiply it and get the answer.

We are calculation this as below

Note – initially, I want to bring this to the notice of all our readers that we have considered $1 equal to 75 Indian rupees with respect to this article.

The terms crores and lakhs are expressed as the following in the Indian number system –

One crore = 1,00,00,000

Ten lakhs = 1,000,000

One lakh = 1,00,000

In the Indian number system, 1 crore is equal to 10 million. It can be also said that one crore is equal to 100 lacs in reference to the Indian number system i.e. 1,00,00,000.

The terms that are used in the international number system are trillion, million, and billion.

Read More

How much is 1 million?
How much is 1 billion in rupees?

On the other hand, the terms used in the Indian number system are crores, lakhs, and thousands.

5 million means

5 million means 5,000 thousand in mathematics. 5 million is a natural number that is preceded by 5000001 and followed by 4999999.

If you do not have a fair idea of the terms used in the international number system, then do not worry as we are here to help you. This generally poses a problem as we do not use these terms in our daily life.

Continue reading to find out 5 million dollars in rupees, 5 million in rupees, 5 million in numbers, 5.5 million dollars in rupees, 5.5 million USD to INR, 5 million dollars in rupees in words, and how much is 5 million.

5 million dollars in rupees

I hope that all of my readers are aware that one trillion is equal to 1000 billion and 1 billion is equal to 1000 million.

You all should also know the following –

One Trillion or thousand billion is equal to 1,00,000 Crores

1000 Billion = 10000000 Lacs

1000 Million or 1 Billion = 10000 Lacs

100 Million = 1000 Lacs

10 Million = 100 Lacs

1 Million = 10 Lacs

Thus, 1,000,000 is ten lacs is one million.

1,000,000 × 5 = 5,000,000 i.e. five million.

75 × 5,000,000 = Five million dollars.

Five million dollars = 375000000 Indian rupees.

5 million in rupees

5 million in words and Indian Rupees are given below –

  • 1 million is equal to 10 lakhs and that is represented as 1000000.
  • 2 million is equal to 20 lakhs and that is represented as 2000000.
  • 3 million is equal to 30 lakhs and that is represented as 3000000.
  • 4 million is equal to 40 lakhs and that is represented as 4000000.
  • 5 million is equal to 50 lakhs and that is represented as 5000000.
  • 6 million is equal to 60 lakhs and that is represented as 6000000.
  • 7 million is equal to 70 lakhs and that is represented as 7000000.
  • 8 million is equal to 80 lakhs and that is represented as 8000000.
  • 9 million is equal to 90 lakhs and that is represented as 9000000.
  • 10 million is equal to 1 crore or 100 lakhsand that is represented as 10000000.
  • 50 million is equal to 5 crore or 500 lakhsand that is represented as 50000000.
  • 100 million is equal to 10 crore or 1000 lakhsand that is represented as 100000000.

1 million in Indian Rupees is equal to 10 lacs. Therefore, for calculating 5 million in Indian rupees we have to use the below-mentioned mathematical formula –

5 million  = 1 Million or 10 Lacs × 5 = 50 lacs Indian rupees

Therefore, 5 million in Indian rupees is equal to 50 lacs or fifty lacs Indian rupees in words.

5 million in numbers

Now, as you know 5 million is equal to 50 lakhs in the Indian number system, now it’s time to discuss 5 million (International number system) or 50 lacs (Indian number system) in numbers.

In numbers, five million can be written or represented as 50,000,00.

5.5 million dollars in rupees

The national currency of India is known as the Indian rupee. If we talked about the currency is at the international level then the United States dollar or the USD is a more popular currency as compared to the Indian rupee.

The dollar rates are never stable and change from time to time in our nation on the basis of the economy of the country.

We have provided you the formula for the calculation of 5.5 million dollars in the Indian rupee below –

5.5 million dollars in rupees = Indian Dollar rate X5.5 million

For example, let’s assume that one USD in our nation is placed at 75 Indian rupees. So, the calculation of 5.5 million dollars is given as below –

5500000 [5.5 Million] × 75 [Indian Dollar Rate] = 41250000 [5.5 Million Dollars in Rupees]

5.5 million dollars in rupees in words is equal to four crores twelve lakhs and Fifty Thousand Indian rupees.

5.5 million USD to INR

As calculated above,

5.5 million USD is 41250000 INR in numbers.

5.5 million USD is four crores twelve lakhs and Fifty Thousand INR in words.

Note – We have taken 75 Indian rupees into consideration as the Indian Dollar Rate for this calculation.

5 million dollars in rupees in words

We will convert 5 million dollars in rupees in numbers and 5 million dollars in rupees in words on the same lines as we have converted 5.5 million dollars in rupees in numbers and 5.5 million dollars in rupees in words before.

So, now I hope that all of you are aware that the value of 5 million dollars in Indian rupees will never be stable as it depends on the dollar rate that is constantly changing.

We would also like to remind you that we have taken the value of the dollar rate as 75 rupees relative to this article.

So, as mentioned above, the following is the formula for the calculation of five million dollars in Indian rupees –

5.5 million dollars in rupees = Indian Dollar rate X5.5 million

For example, let’s assume that one USD in our nation is placed at 75 Indian rupees. So, the calculation of 5 million dollars is given as below –

5000000 [5 Million] × 75 [Indian Dollar Rate] = 37500000 [5Million Dollars in Rupees]

5.5 million dollars in rupees in words is equal to three crores and seventy-five lakhs Indian rupees.

Frequently Asked Questions (FAQs)

How much is 5 million?

5 million (International Number System) is equal to 50 lakhs (Indian Number System). It consists of 6 zeroes. If we go by definition, then 1 million is followed by 6 zeroes.
In numbers, 5 million can be written or represented as 5000000 Indian Rupees.

How much is 1 million: In Rupees thousands lakhs dollars

1 million meaning

In Mathematics, 1 million implies 1 thousand thousand.

If we talk mathematically, then 1 million is a natural number which is preceded by 1000001 and followed by 999999.

We rarely use millions in our daily life unlike lakhs, thousands, and hundreds.

Therefore, to be honest most of us do not have a very good idea about how many zeros are there in a million.

The meaning of the word million is well familiar to both the long scale and small scale numbering system, unlike the big numbers, that have many names in the two types of system that is the Indian number system and the international number system.

By the way, do you know that the word million has been taken from the early Italian million (Modern Italian – milione) and that means ‘thousand’ + the augmentative suffix – one.

For your information, million is abbreviated as m.

We will provide you with all the necessary information regarding what is 1 million in lakhs, rupees, and numbers in order to help you with that.

Continue reading to find out everything about how much is 1 million.

How much is 1 billion in rupees?

1 million in rupees

Million is essentially the term that we use to represent the big numbers in the international number system.

We can also represent millions by using some of the conversions to represent in the Indian number system.

We should take 1 million as 10 lacs in Indian rupees and 1 lacs has 6 zeros to convert millions into rupees.

1 million in words and Indian Rupees are given below –

  • 1 million means 10 lakh that is 1000000.
  • 2 million means 20 lakh that is 2000000.
  • 3 million means 30 lakh that is 3000000.
  • 4 million means 40 lakh that is 4000000.
  • 5 million means 50 lakh that is 5000000.
  • 6 million means 60 lakh that is 6000000.
  • 7 million means 70 lakh that is 7000000.
  • 8 million means 80 lakh that is 8000000.
  • 9 million means 90 lakh that is 9000000.
  • 10 million means 100 lakhs or 1 crore i.e. 100000000.
  • 50 million means 500 lakhs or 5 crores that is 50000000.
  • 100 million means 1000 lakhs or 10 crores that is 100000000.

What is the value of 5 million dollars in Indian rupees?

1 million in lakhs

1 million implies 10 lacs. 1 million in numbers is written as 1000000.

The terms millions, lakhs, and rupees are often used to understandably and easily write a big amount in the number system.

The place value of digits might be treated very differently in the international and the Indian number system (specially in the United States of America).

The place value of digits goes by ones, tens, hundred, thousand, ten thousand, lakh, 10 lakh, crore, 10 crore,s and moreover in the Indian number system.

The place value of digits of numbers goes by ones, tens, hundred, thousand, 10 thousand, 100 thousand 1000 Thousand, and moreover in the international number system.

But you should also know that the number of zeros in both the international number system and the Indian number system is exactly the same.

So, 1 million in the international number system and the Indian National system consists of number 1 preceded by 6 zeros.

1 million in lakh is given below –

  • 1 million means 10 lakhs.
  • 2 million means 20 lakhs.
  • 3 million means 30 lakhs.
  • 4 million means 40 lakhs.
  • 5 million means 50 lakhs.
  • 6 million means 60 lakhs.
  • 7 million means 70 lakhs.
  • 8 million means 80 lakhs.
  • 9 million means 90 lakhs.
  • 10 million means 100 lakhs.
  • 50 million means 500 lakhs.
  • 100 million means 1000 lakhs.

1 million equals

1 million equals 10 lakhs or  1000 thousand. It is represented numerically, as –

1 million = 1000000 = 10 lakhs

1 million (M) = 1000000

1 million is the preceding no to 1000001 and the succeeding no to 999999, such that –

1000001 – 1 = 1000000

999999 + 1 = 1000000

1 × 10⁶ is the scientific notation of 1000000.

1 million dollars in rupees

The currency is known as the rupee in India. Specifically, the dollar or USD is a more popular currency if we talk about international currencies.

On the basis of the economy of the nation, the rate of dollar changes every day in our country India.

Below, you can find the formula to calculate 1 million dollars in Indian rupees –

1 million dollars in rupees = Indian Dollar rate × 1 million

Example: You should assume that 1 United States dollar in India is around 70 rupees. Therefore the calculation of $1000000 is as follows –

70 (dollar rate) × 1000000 (1 million) = 70000000 (1 million dollar in rupees).

1 million pounds to dollars

Here, we have converted 1 million pounds to dollars as per the current foreign exchange rate1.37485014.

For 1 million pounds today, you will receive exactly 1,374,850 dollars 14 cents.

When there will be a change in exchange rates of pounds to dollars, then accordingly the value of 1 million dollars will get changed to dollars.

In this segment, you will come to know that how many lacs make up a single million

How many lacs is 1 million?

There are many different answers to the above-mentioned question.

The money amount is read as rupee, tens, hundreds, thousands, and moreover in the Indian number system.

In nations such as the United States of America, million is the term people use to denote big amounts of money in the International Number System.

However, 1 million is equal to 10 lakhs in Indian rupees and can be also expressed as –

1 million = 0.1 crore

1 million = 10 lacs

1 million = 1000000 rupees

How many thousands are in a million?

One million is equal to one thousand thousand.

The place values of digits in the number go in Ones, Tens, Hundreds, Thousands, Ten thousand, Lakhs, Ten Lakhs, Crores in the Indian Number System.

One million is equal to ten lacs or one thousand thousand. 1 million can be numerically represented as

1 million = 1000 thousand.

1 million is equal to 10 lakhs, which is numerically written as 1000000.

1 million (M) = 1000,000.

Million to billion converter (write steps how to convert)

The SI units, also known as the International System of Units, is a measurement system that establishes a standard for measuring the physical properties of each and every matter.

Ranging from industry to school, number measurements are used in a wide range of settings.

Whether it is for cooking or shopping, units are important in our everyday lives.

Millions to crores to billions calculators make use of multiplicative conversion factors and make it possible to convert several measurement units, such as million to billion, and many more.

You will require a million to billion converter that is both simple and sophisticated to use when you are converting numbers.

It is very simple to convert a million to a billion because you only require to select the amount and the units you wish to convert.

This tool or method will offer you with the exact unit conversion if you are having some issues doing this on your own.

We will also provide you with the formula to convert millions to billions while using this particular converter.

A Million Explained –

A million can be described as a number that is equal to the product of thousand times 100.

If you want, you can also use the number 10⁶ to represent a million. A million is a very big number which follows 100 thousand in the number sequence beginning with 1.

A Billion Explained –

On the other hand, a billion is an amount that is 10 times the size of 1 million. It is 1000 multiplied by 1000000.

It is even possible to compose it as 10⁹. It comes after 1 hundred million in the number chain.

The conversions that are available on such calculators are trillions to crores, millions to lacs, lacs to millions, crores to billions, crores to millions, millions to billions, and many more.

It is faster than anything if you require to convert millions to billions. This method will be advantageous to both professionals and students in the industry of finance.

You can use it as a million to billion converter, an amount to million converters, and a billion to million converter, depending on your conversion requirements.

How do these converters work or The Steps to convert million to billion are –

  • Type in the specified number in the provided input box.
  • Selecta notation from the first dropdown menu.
  • Select an option (a notation) from the second list to convert your number.
  • Tap on the calculate button to get the conversion.
  • Tap on the reset button to enter new values.

You can also use a fraction to decimal conversion for getting a decimal value if you wish to translate a fraction to a billion or a million. Therefore, you can also convert using the decimal value.

Delineation of Billions and Millions –

  • Multiples of 1000

Billion –1000 × 1000 × 1000

Million – 1000 × 1000

  • Power Denomination of 10

Billion – 10⁹

Million – 10⁶

  • Numerical Form

Billion – 1000000000

Million – 1000000

Converting Million to Billion

The expressions trillion, billion, and million are used in the Western or International number system. 

If you don’t know till now, then 1 billion is equal to 1000 million. You need to multiply a number by 0.001 to convert it from a million to a billion.

To do the reverse (to convert a number from a billion to a million), you should simply multiply it by 1000.

1000 Million = 1 Billion

For converting millions to billions,

Million to Billion = 0.001 × Value in Million

Q. Can you tell me that there are how many billion in 200 million?

0.001 × 200 Million = 0.2 Billion

Another example on our list :

Q. Convert 8 m to a billion.

A. 8 million means 0.001 × 8 m = 0.008 billion

Million to Billion –

  • 1 Million means 0.001 Billion.
  • 1.2 Million means 0.0012 Billion.
  • 1.5 Million means 0.0015 Billion.
  • 2 Million means 0.002 Billion.
  • 3 Million means 0.003 Billion.
  • 4 Million means 0.004 Billion.
  • 5 Million means 0.005 Billion.
  • 6 Million means 0.006 Billion.
  • 7 Million means 0.007 Billion.
  • 8 Million means 0.008 Billion.
  • 9 Million means 0.009 Billion.
  • 10 Million means 0.01 Billion.
  • 25 Million means 0.25 Billion.
  • 50 Million means 0 05 Billion.
  • 100 Million means 0.1 Billion.
  • 500 Million means 0.5 Billion.
  • 1000 Million means 1 Billion.

Interest on a million dollars

As of today, the average savings account rate is 0.05% APY. After one year, if you deposit a million dollars with that APY, then it would generate around $500 ($1,000,000 X 0.0005 = $500).

It would generate 5011.27 US Dollars if you left it to compound monthly for a period of 10 years.

1 of 1 million (calculate 1% of 1 million)

So now, let’s calculate what is 1% of 1 million? (One percent of one million?).

How can you calculate 1% of 1 million (in other words)? First of all, you should know that 1% implies 1 per 100, and one million is 1 followed by 6 zeroes.

You need to multiply the number by the percent and then divide the product by a hundred for calculating the percent of a particular number.

For simplification, here is a formula for you –

(Percent × Million) / 100

You should first multiply 1 million by one and then you should divide that product by 100 using the formula. 

Here is the complete mathematics to show you how to do it –

1 × 1 million = 1 Million

1 Million / 100 = 0.01 Million

There you have your answer! Now we will provide you the answer to 1% of 1 million in words (letters) followed by numbers (digits). We start with words –

Ten Thousand

Next, we will provide you the answer in numbers the way you would write it instead of saying it with all those words.

Once again, here is your answer to 1 percent of 1 million in numbers –

10,000

1 million seconds

Many people are lousy with numbers, especially the big and significant numbers.

Numbers such as trillions, billions, or millions are simply hazy notions of really significant numbers for many individuals.

You might actually witness their eyes glaze out and over by simply adding a dollar sign in front of these numbers.

For example, I hope that each one of you knows that a minute is made up of or equal to 60 seconds, and each one of you might also have a good sense that how long a second lasts.

Now if I ask you that how long will a million seconds lasts then do you have the answer to this question?

Here you go :

A million seconds will talk more than a week and a half to elapse (around 12 days).

Now, let’s move to the billion dollar question : How long will a billion seconds last?

A billion seconds will take around 32 years to elapse.

Moreover, a trillion seconds will take 31688 years to elapse.

You are required to start the timer from way back in 29673 B.C. for that to happen!

FYI, 1000000 arc-seconds =277.778 degrees.

1,000,000/25

100000 / 25 is equal to 40000 (forty thousand in words).

How many zeros in a million?

Million is a number that is equivalent to the product of 1000 and 1000 i.e. 1000 × 1000 (1000000) and is used in the international number system.

To answer your question, there are 6 zeroes present in a million.

Look at the following explanation to better understand the concept. It will help you to count the total number of zeroes in a million.

1 million is equal to 1000 thousand.

1000 has three zeros.

Thus, 1 million can also be written as 1000000.

Thus, 1 million i.e. 1000000  has six zeroes.

3 million dollars

Currently, 3 million dollars is equal to 22,30,21,050.00 Indian Rupee (calculation is based on dollar price). In words, it is twenty-two crores thirty lakhs twenty-one thousand, and fifty rupees.

Note – This value has been calculated according to the current foreign exchange rate and the value of USD in the international market.

1 million dollars

Currently, 1 million dollars is equal to 7,43,51,300.00 Indian Rupee. In words, it is seven crores forty-three lakhs fifty-one thousand, and three hundred rupees.

Note – This value has been calculated according to the current foreign exchange rate and the value of USD in the international market.

1 million in Crores

The conversion of currency from millions to crores involves the representation from the international number system to the Indian number system.

However, the place value of digits certainly varies from the International number system to the Indian number system.

Therefore, the conversion of numbers from millions to crores is given as follows.

1 million in crores is written as –

  • 1 million is 0.1 crore.
  • 10 million is one crore.
  • 50 million means 5 crore.
  • 100 million implies 10 crores.
  • 200 million means 20 crores.
  • 500 million means 50 crores.
  • 1000 million means hundred crores.
  • 1 million is equal to 1/10th of a crore.

1 million in Hindi

1 million meaning in Hindi is written as below –

1 million (Hindi) = 10 लाख (10 Lakhs)

Frequently Asked Questions (FAQs)

How much does a million dollars weigh?

We can safely say that a million dollars weigh 1 metric ton.
You should keep in mind that a US ton is equal to 2000 pounds. Therefore, it is safe to conclude that 1 million dollars will weigh in at around 1.1. US tons.

How many millions are in a billion?

A billion is a number that has 2 different definitions –
10⁹ (ten to the ninth power) or one thousand million i.e. 1000000000, as defined on the small or short scale.

How much does YouTube pay you for 1 million views?

YouTube will pay you anywhere between US 3400 dollars to US 40000 dollars for 1 million views on your YouTube videos. The exact amount will depend on a variety of factors such as the number of subscribers, how your channel is performing and growing, daily view counts and subscribers growth count, etc.

How many crores is 1 million dollars?

The answer of this question depends on the value of the US dollar exchange rate as per Indian currency (Rupee) is concerned. If the value of US dollar is Rs. 70 (let’s say), then the value of 1 million dollars is 7 crores Indian rupees. So, likewise you can calculate the value of 1 million dollars as per the value of the US dollar in terms of Indian rupees.

What do you mean by a million in India?

The value of 1 million in India is 1000 Thousand or 10 lacs rupees.

How many lacs is 9 million?

9 million is 90 lacs.

How many millions make 1 billion?

1 billion is 1000 million.

How many lakhs are there in a million?

10 lakh make 1 million.

What is the value of one million?

The value of 1000000 is 1 million.

How many million makes a crore?

1 crore is 100 lacs in the Indian number system. All of us know that 1 million is 10 lakh, so 10 Millions is one crore.

How many zeros are there in 1 million?

As all of us know, 1 million is 10 lacs and 1 lac has 5 zeroes. Therefore, it means that 1 million i.e. 10 lacs has 6 zeroes (1000000).

How many millions make 1 billion?

1000 millions make 1 billion. Also, for your information, 1 million is also the one-thousandth of 1 billion. Simply, we can also say that 10 thousand lacs = 1 billion.

What do you understand by a billion?

In Indian Rupees, 1 billion is equal to 100 crores. If we express 1 billion in terms of millions, then 1 billion is equal to 1000 millions.

What is the true value of 1 million?

The value of 1 million face 1000 Thousand or 10 lacs in Indian rupees or Indian number system. For your information, 1 million is abbreviated as m (that is million). For example, 2 million is written as 2 m.

Definition of circle Circumference, Area, Chord, Segment

Definition of circle

When a line AB rotate by 360 degree taking center A, thus obtained figure is called circle.

A is called center of circle. A to any point on the circle joining is called radius, a line passing through the center of the circle is called diameter of circle and its value is 2 * radius.

The ratio between circumference to diameter is always constant and denoted by \pi its value is \frac{22}{7} or 3.14 approximately.

circle

\frac{pI}/D= \pi

Circumference of circle

so circumference of circle (p)=\pi*D=2*\pi*r

Area of circle formula

Area of circle=\pi*r^2=pi*\frac{d^2}{4}
=4*\pi^2*r^2/4*pi={(2*\pi*r)}^2/4*pi=(oce)^2/4pi

We divide a circle in to many small sectors, thus the length of an arc is reached near about the length of chord.

Then merge them as below we have obtained a ractangle.

Length of Chord

drawit-diagram-5
Length of chord=\frac{a^2+h^2}{2h}
where 2a=lengh of chord
h= height of arc
r=radius of circle
h=r+-\sqrt(r^2-a^2)

length of arc= arc/oce=Angle in degree/360
Radion: If are is equal in length to the radious, then the angle for form are called radion.

Segment of a circle

chord AB of a circle divides the circular region into two part, each part is called a segment of the circle.

segment
Sector of the circle– the area surrounded by an arc and the two radius joining the end point of the arc with the center is called a sector of the circle.
sector

Concentric circle– two or more circles with the given centre are called concentric circle.

Read More

Shapes

Exponent

{2}^{6} – where 2 is the base & 6 is the exponent, and read as “two raised to the power six”
Negative integral exponent of a rational number when a is the non zero R.N
a^{(-n)}=  (\frac{1}{a})^n , (\frac{2}{3})^{-4}=  \frac{1}{\frac{3}{4}}^4
(\frac{a}{b}){-n}= (\frac{b}{a})^n (there is \frac{a}{b} and \frac{b}{a} multiplication inverse)

a^m×a^n=a^{(m+n)} a^m/(a^n  ) = a^{(m-n)} where m > n (a^m )^n=a^{mn}

(ab)^n= a^n*b^n (\frac{a}{b})^n=\frac{a^n}{b^n}

Express the numbers in exponantal form
(a*10)^b where 1<a<10
e.g .008 = \frac{8}{1000} = {8×10}^3
400000 = 4*100000 = (4×10)^5

Square
The square of a number is the product of the number with the number itself
e.g. 1^{2}=1, 2^2  =4, 3^2=9
1,4,9,16,25……… are called perfect square.

To find the perfect square– factorize the given number, if their factors are in pair, then the number is perfect square,
e.g. 36 = 2*2*3*3 is a perfect square.

Number perfect square.

No perfect square will end with 2,3,7,or 8 at the unit place.
A number having 0,1,4,5,6,9, in the unit place may or may not be a perfect number

(1) If the number has 1 or 9 at the unit place than its square and with 1
(2) The square of a number which has 4 or 6 at the units place will and in 6
(3) A number ending in an odd number of zero is never a perfect square.
E.g. 640, 5000, 44000
Between the square of the numbers n and n+1 there are 2n non perfect square numbers
1^2=1 , 2^2  =4 , n=1 ∴2n=2
2^2=4 , 3^2=9 , n=2     ∴2n=4
3^2=9 , 4^2=16 , n=3     ∴2n=6

The square of an even number is always an even number & the square of an odd number is always an odd number.
2^2=4, 3^2=9
The secure of a natural number (expert ) is either or multiple of 3 or exceeds a multiple of 3 & 41
3^2=9=3×3
4^2=16=3×5+1
Similarly- with 4
4^2=16=4×4
5^2=25=4×6+1

The square of natural number ending with five follows a delimit pattern
52 = (0×1) hundred + 25 = 25
152 = (1×2) hundred + 25 = 225
252 = (2×3) hundreds + 25 = 625
352 = (3×4) hundred + 25 = 1225
452 = (4×5) hundred + 25 = 2025

The sum of first nodal natural numbers in n2
Sum of first odd number = 1 =12
Sum of first two odd number = 1+3 = 4 = 22
Sum of first three odd number = 1+3+5 = 9 = 32
The sum of rfirst four oddd number = 1+3+5+> = 16 =42

Look at this pattern whose number include only one.

12 = 1 ___________(= 12)
112 = 121 (1+2+1 = 4 = 22)
1112 = 12321 (1+2+3+2+1 = 9 = 32)
11112 = 1234321 (1+2+3+4+3+2+1 = 16 = 42)
111112 = 121 (1+2+3+4+5+4+3+2+1 = 25 = 52)

Square of these numbers is serially overdraft 1,2,3 …………..equal to the number of its digit & decreases vice verse ………3,2,1
The sum of the digit of their product is also a perfect square.

72 = 49 pattern- when number of digit = 1 than number of 4 = n, & number of 8 = n time +1
672 = 4489
6672 = 444889
666722 = 44448889

Pythagorean triplet
In right angled triangle:-
For any numbewr m>1, (2m, m2-1, m2 +1) is a Pythagorean triplet
If 3, 4, 5
M=2 22-1, 2×2, 22+1

Square root
The square root of the number , is that number, which when multiplied by itself , gives the number as the product.
√x×√x=x we denote the square root of x, by √x , square root is a inverse process, of square.
2×2 = 4 & √(4 )= √(2×2) = 2
Note:- if a number has a natural numbewr as square root then its units digit must be 0,1,4,5,6 or 9. Negative numbers have no square root in the system of natual numbers
e.g √25= ≠5
to find the square root by factorisation method
√16= √(4×4)=4
The number being the perfect square, will have one or more pairs of ther prime factor, write one factor from each pair & multiplied these factors , the product will be the square root of the number e.g√81= √(3×3×3×3)=3×3=9
To find square root by successive substraction method
The sum of the first n odd natural numbers is n2
This method is useful to find the square root of smaller natural numbers.
81-1 = 80
80-3 = 77
77-5 = 72
72-7 = 65
65-9 = 56
56-11 = 45
45-13 = 32
32-15 = 17
17-17 = 0
Square root by division method
e.g.
to find the number of digit in the square root
√((81) ̅ ) = 1 digit = 9
√(2 ̅(25) ̅ )=2 digit=25
√((20) ̅(25) ̅ )=2 digit=48
√(2 ̅8 ̅(224) ̅ )=3 digit=168
Square root of rational numbers(fraction)
√(a/b)= √a/√b
Square root of decimal
We see that 0.2 ×0.2 = 0.04 ∴ √(0.(04) ̅ ) = 0.2 number of digit 1 & root of 4 = 2
Approximate value of square root
We get the square of that number is multiplied by itself x×x = x2
Similarly if a number is multiplied by itself 3 times we get cube of that number x×x×x = x3
Perfect cube:- a natural number is said to be a perfect cube if it is the cube or a natural number.
e.g 13 = 1, 23 = 8, 33 = 27 thus 1,8,27 are perfect cube.
Properties:-
The cube of even numbers are even & odd number are odd.
In a perfect cube each prime numbers appears three times in its prime factorization √27= √(3×3×3)=
Cube of negative numbers is negative
Cube of number ending with 0,1,4,5,6 & 9 also end with the same digit ending with 8 will end with similarly cubes of number ending 3 &7 will end with 7 & 3 respectively.
Smallest number:- some numbers are expressed as the same of two square & sum of two cubes also.
c.g. :-
1729 = 1728 + 1 = 123 +1
1729 = 1000 + 729 = 103 + 93
4104 = 8 + 4096 = 23 + 163, 4104 = 729 + 3375 = 92 + 153
13832 = 5832 + 8000 = 183 + 203, 13832 = 8+13824 = 23 + 243
Cube root of decimal numbers
To find the cube root of aq decimal numbers, write the number in the form of p/q and then find their cube root

Algebraic expression

A combination of constant and variables connected by some or all at the the four fundamental operations, additions, substraction, multiplication & division is called an algabric expression
e.g- 3x + zy

Terms:- the different part of an algebraic expression separated by sign+ or – are called the terms of an expression.
e.g. 3x+2y (term – 3x & 2y)

factor of terms :- we can factroized all terms all terms.-
e.g 3x + 2y
3x = 3×x
2y = 2×y

Types of algebaric expressions.

Monomial– which contains only one term is said a monimial.
Ginomial– which contains two terms e.g. 3x + 2y
Trinomials– which contains three terms – e.g- 3x +2y +z
Quadrinomials – which contains four terms e.g. 2x + 3y + z-6
Polynomials– which contains one or more terms.

Degree of polynomials The highest power of the variable in a polynomials is called its degree.

x^{3}+3, \frac{1}{2}, y^3+1 Here the degree of the polynomial is 3

Linear polynomial– a polynomial of degree is called a linear polynomials. E.g.- x+3

Quadratic polynomials– a polynomials of degree 2 is called a quadratic polynomials.

E.g. (x+2)(x+3) = x2 + 5x + 6

Cubic polynomial– A polynomial of degree 3 is called cubic polynomials.
e.g. degree of the term- 3x =1
2xy = 1+1 = 2
3x2g = 2 = 1 = 3

Algebraic expressions contains one or more forms and each terms contain variable and numerical coefficient, we find the value of terms to put the value of variables.
Equation– a statement of equality which invader one or more variable is called an equation. Terms of left hand side is equal to right hand side e.g – 3x+5 = 8

Solution of an equation e.g. 3x+5=8

(1 )Trial & error method– put the value of variable x, so that L.H.S= R.H.S.
Put the value of x= 1,2,3 who satisfy by the equation
3(1)=5 =8 the value of x= 1 is satisfied equation

(2) (A) if same number or terms is added, substract multiply or divide to both side of equation , the equation remain same (elemination method)
3x+5=8
3x=3(deduct 5 in both side)
X=1 (divid from 3 in both side)
(B) change in the side of required terms.
3x+5= 8
3x= 8-5
3x=3
x = 3/3 = 1

Sets Identity function

The function that associates each real number to it self is called the identity function and denoted by I
I : R \rightarrow R
I(x) = x : x \varepsilon R

The domain and range of the identity function are both equal to R. the graph is a straight line passing through the origin and inclined at an angle of 45^0 with x axis
F(x) = x
F(1) = 1
F(2) = 2
Modulus Functions:-
If f(x) = |x| = {x when x ≥ 0,
-x when x < 0} Is called the modulus function or absolute value function the domain of the modulus function is the set of all real number. & range is the set of all non negative real number R^+ = {x \varepsilon R : x ≥ 03}
(1) If x ≥ 0 the graph coincide. With the graph of
the identity functional (g= x)

If x < 0 it is coincide to the line y = -x

Properties of Modulus Function

1) For any real number x
\sqrt{(x^2 )} = |x|

2) a,b is a positive real number, then

x^2a^2 |x| ≤ a -a ≤ x ≤ a
x^2a^2 |x| ≥ a x ≤ -a or x ≥ a
x^2 < a^2 |x| < a -a < x < a x^2 > a^2 |x| > a x < -a or x > a

a^2a^2b^2 a≤ |x| ≤ b x \varepsilon [-b, -a] u [a,b]
a^2 < a^2 < b^2 a ≤ |x| ≤ b \varepsilon [-b, -a] u [a,b]

3) for real number x and y

|x+y| = |x| + |y| (x≥0 and y≥ 0) or (x< 0 and y< 0)|x-y| = |x| - |y| (x≥0 and |x|≥ |y|) or (x≤ 0 , y≤ 0 and |x| ≥ |y|)|x± y| ≤ |x| + |y||x± y| ≥ |x| - |y|

Greatest Integer Function (Floor Function)
f(x) = [x] for all xεR or ⌊x⌋ is called greatest integer function

for any real number x the smallest [x] to denote the greatest integer less than or equal to x
Domain of the greatest integer function is the set of R to all real number and the range is the set fo Z of all integers as it’s attains only integer value.

e.g. [2.75] = 2, [3]= 3, [0.74] = 0, [-7.45] = -8 etc

Properties :- if n is integer and x is a real number between n and n+1 then

[-n] = -[n]
[x + k] = [x] + k for any integer k
[-x] = -[x] -1

[x] + [-x] = \left\{\begin{array}-1, if x z\\0, x \varepsilon z \end{array}\right.
[x] – [-x] = \left\{\begin{array} 2[x]+1, if x z\\0, 2[x] \varepsilon z \end{array}\right.
[x] ≥ k = x ≥ k where k \varepsilon z
[x] ≤ k = x < k where k \varepsilon z
[x] > k = x ≥ k +1 where k \varepsilon z
[x] < k = x < k where k \varepsilon z
[x+y] = [x] + [y+x-[x] for all x,y \varepsilon R
[x] + [(x+ \frac{1}{n})] +  [(x+ \frac{2}{n})] + ………………..+ [(x+\frac{n-1}{n}] = [n x], n \varepsilon N

Smallest Integer Function
f(x) = ⌈x⌉ for all x εR
Is called the smallest integer function or the ceiling function.

The domain of the smallest integer function is the set of R of all real number and its range is the set z 0 < all integers e.g :- ⌈4.75⌉=5, ⌈-7.2⌉ = -7,⌈5⌉=5, ⌈.75⌉=1 etcProperties of Smallest Integer Function ⌈-n⌉= -⌈n⌉ ,n \varepsilon z

⌈-x⌉= -⌈x⌉+ 1,x \varepsilonR-z

⌈x+n⌉= ⌈x⌉+ n,xεR-z and n \varepsilon z
⌈x⌉+ ⌈-x⌉ = \left\{\begin{array}-1, if x z\\0, x \varepsilon z \end{array}\right.
⌈x⌉- ⌈-x⌉ = \left\{\begin{array} 2[x]+1, if x z\\0, 2[x] \varepsilon z \end{array}\right.

FRACTIONAL PART FUNCTION

The function f(x) = {x} for all xεR
The symbol {x} denote the fractional part of or decimal part of x.
The domain of the fractional part function is the set of R of real number and range is the set [0,1]
f(x) = {x} = x – [x] : x εR
e.g. 3.45 = 0.45, [2.75] = 0.25, [-0.55] = 0.45, [3] = 0, [-7] = 0 etc

SIGNUM FUNCTION

If f(x) = \left\{\begin{array}-\frac{|x|}{x}, x \neq 0  \\0, x= 0  \end{array}\right. .3 × .3 =.09
f(x) = \left\{\begin{array} 1, x > 0  \\0, x= 0 \\ -1 x < 0  \end{array}\right.
The domain of the signum function is the set of R (all real number) and the domain is the set
(-1,0,1)

EXPONENTIAL FUNCTION:-
F (x) = a^x where a> 0 and a ≠ 1
If a > 1
If y = f(x) = a^x \left\{\begin{array} < 1 for x < 0  \\ =1 for x= 0 \\ >1  for x > 0  \end{array}\right.

We observe that – 2^x<3^x<4^x ……………….. : x>1
2^x = 3^x = 4^x …………………. : x = 0
2^x>3^x>4^x ……………….. : x<1

If 0 < a<1Y = f(x) = a^x decrease with the increase in x.
And y>0 : x ε R
a^x \left\{\begin{array} > 1 : x < 0  \\ =1 : x= 0 \\ <1  for x > 0  \end{array}\right.

if z<e<3 then graph

f(x) = e^x    \longrightarrow      f(x) = a^x   : a >1
f(x) = e^x  \longrightarrow        f(x) = a^x   : 0< a<1

Set Relations

A relation (“ is Religion of”) between SET A to SET B is a sub set of A×B
Where ‘R ≤ A×B
If SET A & SET B is not Vol D SET & If (a,b) \varepsalon R read as a is related to b by relation R’ if (a, b) R then a ×b (a is not related to b & y any relation R
Total Number Of Relation: If SET A and SET B not empty finite sets consisting of m and n elements then A×B consists of mn ordered pairs and total no. of sub sets of A×B is 2^{mn}
Among these 2^{mn} relations the void relation \phi & the universal relation A×B are trivial relations from A to B.

Domain And Range Of A Relation– relation to SET A to SET B all first components or co ordinates of the ordered pairs belonging to R is called the domain while the set of all second components or co-ordinates of the ordered pair in the R is called the range of R.

Relation On A Set– A non raid SET- A to relation is set (SET A) = A×A is called a relation on SET A
Inverse relation:- If SET A and SET B two sets and R is relation between them then inverse of R denoted by R^{-1}, is a relation from B to A
R^{-1} = {(b,a): (a,b) \varepsilon R}

Functions: a relation F from SET A to SET B i.e a subset of A×B is called function L or a mapping (or a map) from A to B if

(i) For each a \varepsilon A there exists bε B such that (a,b) f
(ii) (a,b) \varepsilon f and (a,c) \varepsilon f b=c

A non void set f of A×b is a function from A to B if each elements of A appears in some ordered pairs in f and no two ordered pairs in f have the first element.

If (a,b) \varepsilon f then b is called the image of a under f.
e.g. set A= (2,3,4)
set B = (3,4,5)
f1, f2, f3 is three sub set of A×B as below.
f= {(1,2,3), (3,4), (4,5)}
f2 = {(2,3), (2,4) (3,4) (4,5)}
f3= {(2,4), (3,4)}
here f1 is a function from A to B
f2 is not a function from A to B because 2 \varepsilon A has two images 3 and 4 in B.
f3 is not a function A to B because 4 varepsilon A has no image in B.
if a function F is expressed as the set of ordered pair, the domain of f is the set of all first component(elements ) of member s of f & the range of f is the set of second components of member of f.

Function As A Correspondence
If A and B is non empty sets, then a function f from set A to set B is a rule or method or correspondence. Which associate elements of set A to set B such that
(1) All elements of Set A are associated to elements in set B.
(2) An element of set A is associated to a unique element in set B.
If ‘ f ’is a function from a set A to set B then we write f:A \rigtharrow B or A \rightarrow B and read as “f is a function from A to B”.
If an elements a \varepsilon A is associated to an elements bε B then B is called the f image of a’ or image of a under f’ or the value of the function f at a’

A is called the pre image of B under function f & write b = f(a)

Description of a function:- if f:A \rightarrow B be a function such that the set A consists of a finite number of elements than f(x) described by listing the values it attains at different paints of its domain

Domain Co Domain And Range Of A Function:
IF f :A \rightarrow B , then the set A is known as the domain of f and the set B is known as the co domain of f. The set of all of image of elements of A is known as the range of f or image set of A under f and is denoted by f(A)

F(A)= {f(x): x \varepsilon A} = range of f or f(A) ≤ B
e.g. Set A= {-2,-1,0,1,2,} and B= {0,1,2,3,4,5,6}
Consider a rate f(x) = x^2
then f(-2) = (-2)^2 = 4
f(-1) = (-1)^2 = 1
f(0) = (0)^2 = 0
f(1) = (1)^2 = 1
f(2) = (2)^2 = 4

as above each elements of A is associated to a unique elements of B so, f:A \rightarrow B is given by f(x) = x^2 is a function

Here domain (f) = A {-2,-1,0,1,2}
Range (f) = {0,1,4}

EQUAL FUNCTION
Two functions f & g are said to be equal, if
(1) Domain of f = domain of g.
(2) Codomain of f = co-domain of g
(3) F(x) = g(x) for every x beginning to their common domain then function f = function g

Real Function : if domain and co domain are sub set of :
(A) (B)
The set R of all real number , function are called real function.
Domain of real function:- real functions are described. By providing the general for mald for finding the image of elements in its domain.

Range Of Real Function:- the range of a real function of a real variable. Is the set of all real value fallen by f(x) at paints in its domain.
Constant Function:- if K is a fixed real number
Then f(x) = k (x \varepsilon R)
The graph of a constant function f(x) = K is a straight line. Parallel of x – axis above or below of x axis according positive or negative value of K, if k = 0 the straight line is coincident of x axis

Set identity functions

Law of Algebra of sets

Law of Algebra of sets:

a) Impotent law- A \cap A=A and A \cup A = A
b) Identity Law – A \cap \phi = A and A \cup u=A
c) Commutative law- A \cap B = B \cap A and A \cup B = B \cup A
d) Associative law- (A \cap B) \cap C = A \cap (B \cap C)
e) Distributive law- A \cap (B \cup C) = (A \cap B)∩(A \cap C)
– A \cap (B \cap C)= (A \cup B) \cap (A \cup C)

Some Use Full Theorem

If A and B are any two sets then

a) A-B = A \cup B^'
b) B-A=B \cup A^'
c) A-B=A \longleftrightarrow A \cap B =\phi
d) (A-B)\cup B = A \cap B
e) (A-B) \cap B = \phi
f) A \leq B \longleftrightarrow B^{'} \leq A^'
g) (A-B) \cup (B-A) = (A \cup B) – (A \cap B)

Some Important Result on Number of Elements In SETS
If A,B and C are finite sets and u be the universal set then.

1. n(A \cup B) = n(A) + n(B) – n(A \cap B)
2. n(A \cup B) = n(A) + n(B) + n(B) \longleftrightarrow A,B are adjoint non vaid sets.
3. n(A-B) = n(A) – n(A \cap B)
i.e n(A-B) + n(A \cap B) = n(A)
4. n(AB) = number of elements which belong to exactly one of A or B
= n(A-B)(B-A)
= n(A-B) +n(B-A) ……………. [(A-B) and (B-A) are disjoint]
= n(A)- n(A \cap B) + n(B) – n(A \cap B)
= n(A) + n(B) – 2n(A \cap B)
5. n(A \cup B \cup C) =
n(A) + n(B) + n(c) – n(A∩B) –n(B \cap C)-n(A \cap C) + n(A \cap B \cap C)
6. number of elements in exactly two of the sets A,B,C
= n(A \cap B) + n(B \cap C) + n(C \cap A)- 3n(A \cap B \cap C)
7. number of elements in exactly on cot the sets A,B,C
= n(A) + n(B) + n(c) – 2n(A \cap B) –2n(B \cap C)-2n(A \cap C) + 3n(A \cap B \cap C)
8. n( A^{'} \cup B^' ) = n((A∩B)’) = n(u) – n(A \cup B)

Certesian Product Of Sets

Ordered Pair– an ordered pair consists of two objects or elements in a given fixed order
If A&B are any two sets then by an order pair of elements are (a,b) Where a \varepsalon A and b \varepsalon B
The position of a paint in two dimensional plane intercession coordinate is represented by an order pair (-1,5) Where x \varepsalon R and Y \varepsalon r

CARTESIAN PRODUCT OF SETS: if A and B are two non empty sets the set of all ordered pairs (a,b) such as a a \varepsalon A and b \varepsalon B is called Cartesian product of the set A and B and is denoted by AB

A×B = {a,b}: a \varepsalon A and b \varepsalon B}

Example if A= (x,y) and B= (2,3,4) find A×B, B×A, A×A
A×B = {(x,z), (x,3), (x,4), (y,z), (y,3), (y,4)}
B×A= {(z,x), (z,y), (3,x), (3,y), (4,x), (4,y)}
A×A= {(x,x), (x,y), (y,x), (y,y)}
As above (A×B) \cap (B×A) = \phi

Graphical Representation Of Cartesian Product Of Sets
If A = {2,3,4}
B = {3,4}
A×B = {(2,3) (2,4) (3,3) (3,4), (4,3), (4,4)}
To represent A×B graphical, draw to line perpendicular to each X & Y axis and then draw these pairs.
As above n(A×B) = n(A), n(B) = 2×3 = 6 Pair

A×B = \phi \longleftrightarrow A = \phi, B = \phi
A×A×A= {(a,b,c) : a,b,c A}
(a,b,c) is called an ordered triplet

(i) A× (BUC) = (A×B)U (A×C)
(ii) A×(B∩C) = (A×B)∩ (A×C)
(iii) A×(B-C) = (A×B)- (A×C)
(iv) A×B = B×A \longleftrightarrow A=B
(v) A≤B then A×A ≤ (A×B) (B×A)
(vi) A≤ B then A×C ≤ B×C
(vii) A≤B and C≤D than A×C ≤ B × D
(viii) For any set Four A,B,C,D
(A×B)∩ (C×D) = (A∩C) × (B∩D)
For any set A and B
(A×B)∩ (B×A) = (A∩B) × (B∩A)
(ix) For any three set A,B,C
A × (B’UC’) = (A×B) ∩(A×C)
A× (B’∩C’) = (A×B)U (A×C)
(x) If any two non empty sets have n elements in common. Then A×B and B×A have n^2 elements in common.
(xi) If A is non empty set and A×B = A×C
Then B=C

Set relationship

Venn Diagram

first of all a swiss mathematician euler gave an idea to represent a set by the points in a closed curve. Later on British mathematician john venn brought this idea to practice. Such the diagrams drawn to represent sets are called venn ealer diagrams or venn diagram.
In venn diagrams the universal set u is represended by points within a rectangle and its sub sets are represented by the point in closed curve (usually circle) with in the rectangle.

SOME TYPES OF REPRESENTATION

U (rectangle) universal Set
A- Set
B- Sub set of A
B \leq A

are show common element s of set A & set B
intersecting area = A \cup B
suppose u = {1,2,3,4,5,6,7,8,9,10}
Set A = {2,3}
Set B = {6,7,8}
A \cup B =\phi

OPERATIONS ON SETS

1) Union of sets:
A & B be two sets the union of A & B is the set of all those elements which belong either to A or B or the both A & B.
A \cup B = {x:x \varepsilon A or x \varepsilon B} (A union B)
: x \varepsilon A \cup B \longleftrightarrow x \varepsilon A or x \varepsilon B
And x \varepsilon A \cup B \longleftrightarrow xA and xB
As above A \cup B = B (if A \subset B)
A \cup B = A (if B \subset A)

e.g if A = {1,2,3}
B = {1,3,5,7}
Then A \cup B = {1,2,3,5,7}

2) Intersection of sets: A & B be two sets the inter section of A & B is the set of all those elements that belong to both A & b and denoted by A \cap B

Thus A \cap B = {x:xεA and xεB}
Or x \varepsilon A \cap B \longleftrightarrow x \varepsilon A and x \varepsilon B
Or A \cap B ≤ A and A∩B ≤ B
e.g if Set A = {1,2,3}
Set B = {1,3,5,7}
Then A \cap B = {1,2,3,5,7}

3) Disjoint set: Two set A & B are said to be disjoint if A \cap B= \phi
If A\cap B \neq \phi then A and B are said to be intersecting or over capping sets.

4) Difference of sets:

Symmetric difference of two sets:- if A and b be two set s. then symmetric difference of set A and B is A \bigtriangleup b = (A-B) \cup (B-A)
= {x:x A \cap B}
e.g. Set A = {1,2,3,4,6}
Set B = {2,3,4,5,6,7}
Then A \bigtriangleup B = (A-B) \cap (B-A)
= {1,} \cap (5,7)
A \bigtriangleup B = {1,5,7}

5) complement of a set– If u is the universal set & A is a set such that A \< U than the complement of set A with respect to set u = A^' or A^C or U-A

Thus = A^' = { x \vaarepsalon u : x A}

e.g- if u = {1,2,3,4,5,6}
A= {3,4}
A^' = {1,2,5,6}

Thus u^' = \phi
\phi^'= u
(A^')' = A
A \cup A^' = u
A \cap A^' = \phi

Law of algebra of sets