**What are Numbers?**

Within our everyday routines, we use numerals. They are frequently referred to as numbers.

We can’t count objects, calendars, age, cash, or anything else without numerals. These digits are often used for measuring and several other situations for labeling.

Numbers have features that allow them to conduct numerical calculations on them.

These figures are given both numerically and in utterances. For instance, 4 is written as four, 98 is written as ninety-eight, and so on.

To understand further, students must learn how to write the numerals from 1 to 100 in syllables and by spelling.

There are several sorts of numbers that we study in Mathematics. Natural and whole numerals, odd and even numerals, rational and irrational numerals, etc., are all examples.

In this post, we’ll go through all of the various sorts. Aside from that, numbers are utilized in a variety of industries, including sequence, arithmetic formulas, and so on.

**Types of Numbers**

The number system is a way of categorizing numerals into groups. In math, there are several distinct sorts of numbers:

•**Natural Numerals:** Natural numbers are accounting numbers made up of positive numerals ranging from 1 until ∞. The group containing natural numbers is symbolized by the letter “N,” and it consists of N = 6,7,8,9…….

• **Whole Numerals**: Whole numbers are non-negative numbers that have no fractional or decimal components. It is represented by the letter “W,” and the group of whole numbers contains W = 0, 1, 2, 3, 4, 5,………..

• **Integers:** The collection of all whole numerals, as well as a negative group of natural numerals, is known as integers. Integers are represented by the letter “Z,” and the group of integers can be represented as Z = -2,-1,0,1,2.

• **Real Numbers:** Real numbers are all positive and negative numerals, fractions, and decimal values that do not contain imaginary values. The letter “R” is used to signify it.

• **Rational Numbers:** Rational numbers are any numerals that may be represented as a relation of one value to another value. Any integer that may be expressed in terms of p/q complies with the requirement to be a rational number. The rational number is represented by the letter “Q.”

• **Irrational Numbers:** Irrational numbers are those which can be stated as a proportion of one to another and are denoted by the letter “P.”

• **Complex Numbers:** Complex numbers “C” are values that may be represented as a+bi, in which “both a,b” are real values and “i” is an arbitrary value.

• **Imaginary Numbers:** Imaginary numbers are complex numbers that may be expressed as a combination of a real value and the imaginary component “I.”

**Whole number** All natural numbers including zero are called whole numbers.

Properties of whole number:-

**Addition**– closure property- the sum of whole numbers is always a whole number.

Commutative property- a+b = b+a

Associative property- (a+b)+c = a+(b+c)

Identity element- if zero is added to any whole number the sum is the number itself.

0+a = a+0 = a**subtraction** – closure property- the difference of two whole numbers is not necessary a whole number a-b ≠ b-a not necessary a whole number.

Commutative property a-b ≠ b-a is not defined.

12-4 ≠ 4-12 is not defined.

Property of zero- 0-a ≠ 0-b is not defined.

Associative property- (a-b)-c ≠ a-(b-c)

**Division**– Dividend- the number which is to be divided is called a dividend.**Divisor**– the number by which dividend is divided is called the divisor.**Quotient**– the number of times the divisor is contained in the dividend is called the quotient.**Reminder**– the leftover number after division is called the reminder.

Thus, the relationship between these terms.

**Fractions** The numbers in the form of a/b where a and b are whole numbers and

**Rational numbers** The numbers in the form of a/b a where a and b are integers.

Fractions are also rational numbers a is called the numerator and b is called denominator

equivalent rational number .

**Relational numbers between two relational numbers**

If given two relational numbers are a and b then is relational number between a and b.

Example

and

**More that one relational numbers between two rational numbers**

Write and rational numbers between and

Convert two given rational number into equivalent form with common denominator

To obtain 4 Relational numbers between them multiply numerator and denominators with (4+1=5) to make equivalent relational numbers(Multiply n+1 times where n is required number of relational number between two relational number)

and

then

and

**Relational numbers addition and subtraction**

where the denominator of Relational numbers is greater.

**Relational numbers multiplication****Relational numbers division**

**Factor**– A factor of a number is an exact divisor of the number. Itself in other word the number that are multiplied to get a product are called the factor . for e.g.- 1,2,3,4,6&12 are the factors of 12.

Multiple- a multiple of a number is a number obtained by multiplying it by a natural number. If we multiply 4 by 1,2,3 we get 4,8, 12 which we all multiple of 4.

**Even number**– A natural number which is exactly divided by 2 is called an even number.**Odd number**– A natural number which is not exactly divisible by 2 is called an odd number.**Prime number**– A natural number which is greater than 1 & whose only factors are 1 and the number itself is a prime number.**Composite number**– The number having more than two factors are called composite numbers.**Co-prime numbers**– The two numbers which has no common factor other than one are called co-prime number (2,3) (3,4)

Further research into numbers shows that some more numerals exist in addition to the ones listed previously, such as even and odd digits, prime numerals, and composite numerals. They are discussed below:

**Even Numbers:**Even numbers are numerical values that are perfectly divisible by two. Positive or negative numbers, like -92,-38,6,18,24, 28, etc., are some examples of even numbers.**Odd Numbers**: Odd numbers are numerical values that are not perfectly divisible by two. Positive and negative numbers, like -1,-17,13,15,21,23, are some of the examples of odd numbers.**Prime Numbers:**The numerals with only two factors are known as prime numerals. 1 and the digit itself, to be precise. In other terms, prime numbers are the result of dividing a value by one and the value itself. 13,19,53,61,89 are all prime numbers within 100 number.**Composite Numerals:**A composite value consists of 3 or more factors. For instance, the value 15 is a composite number since it is divisible by 1,3,5 and 15. 44,66,91,82,36 are some of the composite numbers under 100 digit value.

There are some special numbers in mathematics as well,

**Cardinal Numbers:** A cardinal value means the number of units in a sequence, like fifty, thirteen,sixty, seventy, etc., are some of the examples of cardinal values under 100 digit value.

**Ordinal Numbers**: To describe the place of anything in a list, we use ordinal numbers. For example, 20th will be written as twentieth.

**Nominal Numbers:** The term “nominal number” refers to a number that is solely referred to as a name. It has no bearing on a thing’s real value or placement.

**Pi:** Pi is a unique number that is roughly equivalent to 3.14. The proportion of the circumference of a circle reduced by the diameter of a circle is known as Pi ().

Circumference/Diameter = 3.14.

**Euler’s Number (e):** Euler’s number is roughly equivalent to 2.71, and it is among the most important metrics in mathematics. It is the root of the natural log and is an irrational numeral.

**Golden Ratio:** The golden ratio is really a unique number that is roughly equivalent to 1.618. It’s an irrational numerical with no discernible pattern among the numbers.

**Various properties of numbers **

For real values, the characteristics of numbers are mentioned clearly. The following are some of the shared properties:

**Commutative Property**: If a and b represent two actual values, then the commutative principle states that their sum or multiplication is equal.

a + b = b+a

b.a = a.b

4+5 = 5+4 and 4.5 = 5.4 are two examples.

**Associative Property**: If a, b, and c represent three real values, then the associative principle states that

(a+b)+c = a+(b+c)

(a.b).c is the same as a.(b.c)

(4+5)+6 = 4+(5+6), (4.5).6=4.(5.6) are two examples

**Distributive Property:**If a, b, and c represent 3 real values, then the distributive principle states that a

a*(b+c)=a*c+a*c

We can verify the above principle as,

4*(5+6)=4*5+4*6

4*11=20+24

44=44

L.H.S=R.H.S

**Closure Property**: If one value is added to some other, the output is a single number, as in a+b = c, where a, b, and c represent 3 real values.

5+6=11 is an example.

**Identity Property:**The identity property states that if we multiply a number by one or we add zero with it, the result will be the same.

x+0= x

x.1=x

7+0 Equals 7 and 7 x 1 = 7 are two examples.

When a positive number is added by the negative value, the outcome is zero.

0 = x+(-x)

5+(-5) = 5-5 = 0 as an example

**Inverse Multiplication:** When a number other than 0 is multiplied by its own reciprocal, the outcome is 1.

1 = x * (1/x)

50 x (1/50) = 1 as an example

**Property of Zero Product:** When x.y = 0, either x or b must be 0.

For instance, 9 x 0 = 0 as well as 0 x 10 = 0

**Reflexive Property:** The value mirrors the digit itself.

x=1

12=12 is an example.

**Indian Numeral System**

Consider integer 111 as an example. It’s worth noting that the digit 1 appears thrice in this integer. They each have a distinct worth. We distinguish them by mentioning their positioned value, which can be specified as a digit’s numerical value based on its location in a number. As a result, the leftmost one has a place value of hundreds, whereas the one in the middle has a place value of tens, and the one on the right side has a place value of ones.

Returning to the Indian numeral concept, digits have place values of Ones, Tens, Hundreds, Thousands, Ten Thousand, Lakhs, Ten Lakhs, Crores, etc.

The positional meanings of each digit in the integer 12,48,94,231 are:

- 1 – Ones

- 3 – Tens
- 2 – Hundreds
- 4 – Thousands
- 9 – Ten Thousand
- 8 – Lakhs
- 4 – Ten Lakhs
- 2 – Crores
- 1 – Ten Crores

**International Numeral System**

As in international numeral standard, digit place values are assigned to Ones, Tens, Hundreds, Thousands, Ten Thousand, Hundred Thousands, Millions, Ten Million, and so on. The position values of every digit in the number 30,264,019 are:

- 9– Ones
- 1– Tens
- 0 – Hundreds
- 4 – Thousands
- 6 – Ten Thousand
- 2 – Hundred Thousands
- 0 – Millions
- 3 – Ten Million

**How was Zero Number discovered?**

0 (zero) is an integer as well as a numeric value used to depict it in numbers. Zero is a number that denotes the lack of all other numbers. It is the identity component of fractions, real values, and several other arithmetic frameworks and hence plays a crucial role in maths. In position value systems, zero is often used as a temporary replacement, just like a digit.

Aryabhata was a famous Mathematician-Astronomer during the ancient period. He is recognized as one of the finest mathematicians of all periods, having been born in Pataliputra, Magadha. Aryabhata became eternal after giving the public the numeral “0” (zero). The Aryabhatiya, his treatise, contained astronomical and mathematical ideas in which the Globe was assumed to be rotating on its axis, and the planets’ cycles were calculated in relation to the rotation of the sun.

The guidelines for working with integer zero are as follows. Unless otherwise indicated, these laws apply to any complex number x.

**Multiplication:**a + 0 = 0 + a = a (In other words, when it comes to addition, 0 is the identity component.)**Subtraction rules**: a-0 = a and 0-a = -a.**Multiplication**: a.0=0.a=0**Division:**For nonzero a, divide by 0 / a = 0. However, a/ 0 is undefined since, as a result of the preceding criterion, 0 doesn’t have a multiplicative inverse. For positive a the quotient rises toward positive infinity as b in a / b tends to zero from positive numbers, while when b tends to zero with negative numbers, the quotient rises toward -∞. Division with zero is indeterminate, as evidenced by the various quotients. Exponentiation: a.0 = 1, with the exception that in rare cases, the condition a = 0 may indeed be left undetermined. 0.a Equals 0 for any positive number a.**Note:**The multiplication of 0 integers equals 1, while the total of 0 numbers equals 0.

**Here are the Names spellings of numbers from 1 to 100**

1 = One | 2 = Two |

3 = Three | 4 = Four |

5 = Five | 6 = Six |

7 = Seven | 8 = Eight |

9 = Nine | 10 = Ten |

11 = Eleven | 12 = Twelve |

13 = Thirteen | 14 = Fourteen |

15 = Fifteen | 16 = Sixteen |

17 = Seventeen | 18 = Eighteen |

19 = Nineteen | 20 = Twenty |

21 = Twenty-one | 22 = Twenty-two |

23 = Twenty-three | 24 = Twenty-four |

25 = Twenty-five | 26 = Twenty-six |

27 = Twenty-seven | 28 = Twenty-eight |

29 = Twenty-nine | 30 = Thirty |

31 = Thirty-one | 32 = Thirty-two |

33 = Thirty-three | 34 = Thirty-four |

35 = Thirty-five | 36 = Thirty-six |

37 = Thirty-seven | 38 = Thirty-eight |

39 = Thirty-nine | 40 = Forty |

41 = Forty-one | 42 = Forty-two |

43 = Forty-three | 44 = Forty-four |

45 = Forty-five | 46 = Forty-six |

47 = Forty-seven | 48 = Forty-eight |

49 = Forty-nine | 50 = Fifty |

51 = Fifty-one | 52 = Fifty-two |

53 = Fifty-three | 54 = Fifty-four |

55 = Fifty-five | 56 = Fifty-six |

57 = Fifty-seven | 58 = Fifty-eight |

59 = Fifty-nine | 60 = Sixty |

61 = Sixty-one | 62 = Sixty-two |

63 = Sixty-three | 64 = Sixty-four |

65 = Sixty-five | 66 = Sixty-six |

67 = Sixty-seven | 68 = Sixty-eight |

69 = Sixty-nine | 70 = Seventy |

71 = Seventy-one | 72 = Seventy-two |

73 = Seventy-three | 74 = Seventy-four |

75 = Seventy-five | 76 = Seventy-six |

77 = Seventy-seven | 78 = Seventy-eight |

79 = Seventy-nine | 80 = Eighty |

81 = Eighty-one | 82 = Eighty-two |

83 = Eighty-three | 84 = Eighty-four |

85 = Eighty-five | 86 = Eighty-six |

87 = Eighty-seven | 88 = Eighty-eight |

89 = Eighty-nine | 90 = Ninety |

91 = Ninety-one | 92 = Ninety-two |

93 = Ninety-three | 94 = Ninety-four |

95 = Ninety-five | 96 = Ninety-six |

97 = Ninety-seven | 98 = Ninety-eight |

99 = Ninety-nine | 100 = One hundred |

**Why is it important to name the number’s?**

Each student must be familiar with the titles of the numerals. These are essential math skills that will assist children inappropriately spelling numbers. They can also readily write such values when they participate in lessons, and their professors spell them out.

In math’s, integers are extremely important. These numbers provide the foundation for all algebraic and numeric processes, not just in basic school but also in secondary ed.

**How can I learn Number Names from 1 to 100 Easily?**

All you have to do is assist your children in memorizing the digits up to 20, and then a sequence is established from Thirty to 100, as shown below:

1 To 10 Number Names | There is no secret to mastering them. You must assist them in memorizing the digits. |

11 To 20 Number Names | Eleven and twelve are distinct examples, however thirteen to 19 show a pattern, i.e. the value with a teen. Like-Thirteen, Fourteen, Fifteen, Sixteen, Seventeen, Eighteen, Nineteen, and Twenty. |

21 To 30 Number Names | Now a pattern emerges, such as twenty plus one, twenty plus two, and so on… |

31 To 40 Number Names | Same pattern i.e. Thirty + one, Thirty + two…… Thirty + nine… |

41 To 50 Number Names | Forty + one, Forty + two, …. Forty + eight, Forty + nine |

51 To 60 Number Names | Fifty + one, Fifty + two, …. Fifty + eight, Fifty + nine |

61 To 70 Number Names | Sixty + one, Sixty + two, …. Sixty + eight, Sixty + nine |

71 To 80 Number Names | Seventy + one, Seventy + two, …. Seventy + eight, Seventy + nine |

81 To 90 Number Names | Eighty + one, Eighty + two, …. Eighty + eight, Eighty + nine |

91 To 100 Number Names | Ninety + one, Ninety + two, …. Ninety + eight, Ninety + nine |

**Properties of Whole Numbers:**

•The digit 0 is the lowest, and initializing whole numbers, as well as all-natural numbers, including zero, are referred to as whole numbers.

• There is no such thing as a culminating or biggest whole number.

• Because whole numerals are indefinite, there is no greatest whole numeral.

• There is an unlimited amount or an unimaginable range of whole numerals.

• Every Natural Number is a whole numeral.

• Each digit is one higher than the one before it.

• Each Whole number is not a Natural number.

**Examples of Numbers from 1 to 100**

**Example 1:**

Spell 44 digit.

**Solution:**

In digit 44, one’s place is taken by 4, and tens place is also taken by 4. So 4 tens and 4 ones are equal to 44, and we can spell 44 as ‘forty-four.’

**Example 2: **

Write, 18, 20, 14, 200, 5000, 18000, and 60000 in words.

**Solution:**

- 18 in words – Eighteen
- 20 in words – Twenty
- 14 in words – Fourteen
- 200 in words – Two Hundred
- 5000 in words – Five thousand
- 18000 in words – Eighteen thousand
- 60000 in words – Sixty thousand

**Example 3:**

**By using Number system represent 8,299,213,811,552**

**Solution:**

In the starting, the first digit is 8. It is present in the place of a trillion – eight trillion

The next comma to the right side is billion – two hundred ninety-nine billion

The next comma to the right side is million – two hundred thirteen million

The next comma to the right side is thousands –eight hundred eleven thousand

The comma present on the rightmost side represents – five hundred and fifty-two

**8,299,213,811,552 **in number system format is eight trillion, two hundred ninety-nine billion, two hundred thirteen million, eight hundred eleven thousand, five hundred and fifty-two.

**Example 4:**

A student did a study and concluded that the number of users of laptops in Russia in a week in the year 2015 was 456643218. Write it in the number system.

**Solution:**

After applying the commas, the numeral is represented by 456,643,218.

Millions– four hundred and fifty-six million

Thousands– six hundred and forty-three thousand

One’s Place – two hundred and eighteen

The number of users of laptops in Russia in a week in the year 2015 was four hundred and fifty-six million, six hundred and forty-three thousand, two hundred and eighteen(456,643,218).

**Example 5:**

**Following statements of numbers are given write their numeric value**

a] Ninety-four million, five hundred seven thousand, nine hundred thirty-one

b] Eight billion, one hundred thirty-five million, eighty-two thousand, three hundred forty-five

**Solution:**

a] Ninety-four million, five hundred seven thousand, nine hundred thirty-one

The Numeric Value is 94,507,931.

b] Eight billion, one hundred thirty-five million, eighty-two thousand, three hundred forty-five

The Numeric Value is 8,135,082,945.

**Example 6:**

**Choose the correct option:**

Ninty billion two hundred thirty-five million four hundred thirteen thousand four hundred five

a] 90,235,413,405

b] 9,023,514,301 ,405

c]90,235,403,405

**Solution:**

The correct option is 90,235,413,405

**Example 7:**

**Give the numerical value of the following statements:**

a] The distance between Earth and Sun is around 58 billion km.

b] The net weight of a navy ship is 204 km pounds.

**Solution:**

**The situations can be represented according to the number system as:**

a] The distance between Earth and Sun is approximately 58 billion km.

According to the number system, it is 58,000,000,000 km

b] The net weight of a navy ship is 305 km pounds.

According to the number system, it is 305,000,000 km

**Example 8:**

**New York’s reserve fund is around 555 trillion dollars. Write the reserve fund according to the number system?**

**Solution:**

**New York’s reserve fund is around 555 trillion dollars**.

Be sure to take care of commas or periods; three digits are given in billions.

To express the value in the number system, the rest values of millions and others are made zero.

555 billion

Millions – 000

Thousands – 000

Ones – 000

The budget announced was about 555,000,000,000 dollars.

**FAQs – Frequently Asked Questions**

**Check these most asked questions on the webpage:**

**Q1) How do you write 450 in words?**

**A1) 450 is written as Four Hundred Fifty.**

**Q2) How to write 9 in English?**

**A2) Nine**

**Q3) How can I spell 15?**

**A3) 15 is spelled as Fif+teen= Fifteen**

**Q4) Is there any use of learning number system?**

**A4)****Digits can be used to quantify, weigh, classify, and organize items, as well as for barcodes and license plates. Even primitive civilizations placed graphs or charts on items to indicate that they were counting things, if it was weeks, recording transactions, or anything else. There is also indications that the digits were utilized by early Bablyonians and Romans for different uses.**

We can use the numbers practically in following forms-

- A laptop translates any characters, phrases, or passwords into a defined numerical notation, which is incredibly useful.
- Digits assist us in expressing or displaying the accurate estimation of any thing.

- A quantitative data collection method is used to arrange or display distinct elements in a specific sequence.