Number

Definition

It is a mathematical symbol that is used to count, measure, and label/sort/order. There are different kinds of numbers such as.

• Natural Numbers
• Whole Numbers
• Integers
• Rational Numbers
• Irrational Numbers
• Real Numbers
• Complex Numbers

Examples

Example of numbers are 1, 2, 3, 4, 5, 6, 7, 8, 9, 0.

Need of Numbers

Ancient humans used to count animals and other useful things by marking on bones, woods, stone, or walls. To count things, they used to draw a line ( | ) for one and similarly four such lines they would draw and the fifth line would be a cross over others straight lines to show that the set of 5 has been completed. Although this method was feasible or practicable, however, for large counting this method was ill-considered.

Brief History

The evolution of today’s numbers, that are 0,1,2,3,4,5,6,7,8,9, can be traced back. In ancient times, there were numeral systems developed to represent numbers. The first such known system was the Egyptian ciphered numeral system, followed by the Greeks’ Ionic / Ionian / Milesian / Alexandrian Numerals. Later, the Roman numeral system remained popular throughout Europe until in the 1st and 4th centuries, the Indian mathematicians introduced the Hindu-Arabic Numeral System.

Al-Khwarizmi and Al-Kindi were amongst the other Muslim mathematicians who spread the Hindu-Arab Numeral System in Europe through their books. Thus, this system of numeration was famous by the name ‘Arabic Numerals’ in Europe.

Uses of Numbers

Following are some uses of numbers.

• They are accepted and understood globally by everyone irrespective of the region they may belong to.
• Using numbers helps us to predict data and analyze the statistics better.
• It is used in phone numbers, or mobile numbers to keep the identity of the caller different from others.
• Every locker uses a number which distinguish it from other lockers and the owner must remember his locker number to avoid confusion.
• Bar code, which primarily consist of numbers, is used in marts to identify things and in hospitals to give each patient their identity.
• Numbers are basics for mathematics and its related subjects.
• Numbers are used to show weather or human body temperature.
• Books’ pages are also given numbers called page numbers
• In sports, numbers are used to show the score of a player or sportsman / sportswoman.

Number Words

Definition

Number words are the representation of numbers in word form. It is also called ‘number in words’ or ‘number names’. For example, we can represent the number 1 in words as ‘One’. Similarly, the number 0 can be written as ‘Zero’.

Rules

To write any number in words or figures we must follow some rules or steps. Those are.

Rule 1:

Always remember the position of a digit or number such as unit, tens, hundreds etc. If the number is a single digit it must belong to category of 0 – 9 and it is always in units or one’s place. Similarly, if it is a two-digit number, it must be in the range of 10 – 99 and it can be written in both unit and ten columns.

• 1 – Ones / Units column.
• 10 – Tens and Unit column from left to right.
• 100 – Hundred, tens, and unit’s column from left to right.
• 1000 – Thousand, hundreds, tens, and unit column from left to right.

Ten Thousand	Thousand	Hundred	Tens	Unit
1	0	0	0	0

Rule 2:

For the numbers between 0 – 20, we must remember their names such as, zero, one, two, three, four, five, six, seven, eight, nine, ten, eleven, twelve, thirteen, fourteen, fifteen, sixteen, seventeen, eighteen, nineteen, twenty. We can always refer to the number chart below.

Rule 3:

We have special names for these multiple of tens; 10, 20, 30, 40, 50, 60, 70, 80, 90, 100. They are ten, twenty, thirty, forty, fifty, sixty, seventy, eighty, ninety, hundred.

Rule 4:

For the rest of numbers i.e., 21 – 29 we write the prefix twenty which is followed by one, two, three for 21, 22, 23. Similarly, for 31 – 39 we use the prefix thirty and followed by one, two, three for 31, 32, and 33 respectively. This rule applies to 41 – 49, 51 – 59, 61 – 69, 71 – 79, 81 – 89, 91 – 99, using the prefixes forty, fifty, sixty, seventy, eight, and ninety respectively.

Rule 5:

Numbers above 100 uses the same prefix rule, however, there is no exception or special name for 110, 120, 130, 140, 150, 160, 170, 180, …. Rather, we repeat the special names mentioned in rule 2 and 3. So, prefix one hundred (or hundred) followed by ten, twenty, thirty, forty, fifty, sixty, seventy, eighty, …. For a number between 100 – 110 we can explain it by an example.

Hundred	Tens	Unit
1	0	2
One hundred two

For a number between 110 – 120, let us take an example of 113. We have 13 in the tens place; we can use rule number 2. Prefix hundred will be used.

Hundred	Tens	Unit
1	1	3
One hundred thirteen

For a number between 150 – 160, we pick 159 as an example. We have 59 in the tens place which can be written in words as nine preceded by the prefix fifty according to rule number 4. We also have a one in the hundred places, so we will use the prefix hundred as well.

Hundred	Tens	Unit
1	5	9
One hundred fifty-nine

Rule 6:

It can be called as the big number rule. We have special names for big numbers such as thousand for 1000, a million for 1,000,000, a billion for 1,000,000,000.

 Numbering Systems

The basic rules are the same, however, to represent a larger number such as 100000, 1000000, we use two systems which can be used for numbering i.e., writing numbers into words. Those are the international numbering system and the Indian numbering system.

International Numbering System

The international numbering system is used globally. This numbering system uses the same rules as described above, however, for a large number such as 1000 thousand is called Million. 1000 million is called trillion.

In terms of power, the international system can be expressed as 10⁰, 10¹, 10², 10³, 10⁴, 10⁵ for one, tens, hundreds, thousands, ten thousand, hundred thousand. Rest of the higher powers uses a general formula which is 10⁶⁺³ⁿ. If n=0, it is 10⁶ which corresponds to one Million. If n=1, term simplifies to 10⁹ which is one Billion (1000 million). Similarly, for n=2, it is one trillion (1000 billion) and for n=3, it is one Quadrillion (1000 trillion).

Separator is a comma that is placed in bigger or larger numbers. When writing a number without separations there is high chances of a digit being ignored or missed. Therefore, a separator or simply a comma ( , ) is used to avoid confusion while writing large numbers.

In the international system for numbering, a separator is placed every three digits from right to left. For example

• 531,164 – Five hundred and thirty-one thousand, one hundred and sixty-four.
• 10,112,884 – Ten million, one hundred and twelve thousand, eight hundred and eighty-four.
• 3,678,329,414 – Three billion, six hundred and seventy-eight million, three hundred and twenty-nine thousand, four hundred and fourteen.
• 679,391,284,333 – Six hundred and seventy-nine billion, three hundred and ninety-one million, two hundred and eighty-four thousand, three hundred and thirty-three.

Hundred Billion	Ten Billion	Billion	Hundred Million	Ten Million	Million	Hundred thousand	Ten thousand	Thousands	Hundreds	Tens	Ones
						5	3	1	1	6	4
				1	0	1	1	2	8	8	4
		3	6	7	8	3	2	9	4	1	4
6	7	9	3	9	1	2	8	4	3	3	3

Indian Numbering System

Indian numbering system is most widely used in the countries like India, Pakistan, Bangladesh, Bhutan, Maldives, Nepal. In the Indian numbering system, we use the term one Lac for 100,000. Similarly, we use ten Lac for 1000000, One Crore for 10 million.

The Indian numbering system can be expressed in the powers of 10 such as 10⁰, 10¹, 10², 10³, 10⁴ for ones, tens, hundreds, thousands, ten thousand. Higher power of 10 uses a general formula for their naming which is 10⁵⁺²ⁿ, meaning that for every odd power of 10, we will have a different name for the number. For n=0, formula becomes 10⁵ which is called One Lac (lakh). For n=1, the general formula reduces to 10⁷ which is One Crore. It continues as 10⁹ for Arab, 10¹¹ for Kharab.

In the Indian numbering system, separators are used differently than the international system. Starting from the right most digit, first separator is after three digits, then separator is placed every two digits. For example

• 4,29,124 – Four lakhs, twenty-nine thousand, one hundred and twenty-four.
• 1,00,12,981 – One Crore, twelve thousand, nine hundred, and eighty-one.
• 1,21,42,56,126 – One Arab, twenty-one crore, forty-two lakhs, fifty-six thousand, one hundred, and twenty-six.
• 4,23,56,76,91,999 – Four Kharab, twenty-three Arabs, fifty-six crores, seventy-six lakhs, ninety-one thousand, nine hundred, and ninety-nine.

Kharab	Ten Arabs	Arab	Ten Crores	Crores	Ten Lakhs	One Lakhs	Ten thousand	Thousands	Hundreds	Tens	Ones
						4	2	9	1	2	4
				1	0	0	1	2	9	8	1
		1	2	1	4	2	5	6	1	2	6
4	2	3	5	6	7	6	9	1	9	9	9

Number Words Chart 1 – 10

The numbers from 1 to 10 are expressed in words in the following table.

Number	Words	Number	Words
1	One	6	Six
2	Two	7	Seven
3	Three	8	Eight
4	Four	9	Nine
5	Five	10	Ten

Number Words Chart 11 – 20

The numbers from 11 to 20 are expressed in words in the following table.

Number	Words	Number	Words
11	Eleven	16	Sixteen
12	Twelve	17	Seventeen
13	Thirteen	18	Eighteen
14	Fourteen	19	Nineteen
15	Fifteen	20	Twenty

Number Words Chart 21 – 40

Numbers from 21 to 40 in words are given in the following table.

Number	Words	Number	Words
21	Twenty-One	31	Thirty-One
22	Twenty-Two	32	Thirty-Two
23	Twenty-Three	33	Thirty-Three
24	Twenty-Four	34	Thirty-Four
25	Twenty-Five	35	Thirty-Five
26	Twenty-Six	36	Thirty-Six
27	Twenty-Seven	37	Thirty-Seven
28	Twenty-Eight	38	Thirty-Eight
29	Twenty-Nine	39	Thirty-Nine
30	Thirty	40	Forty

Number Word Chart 41 – 60

Number in words from 41 to 60 are in the following table.

Number	Words	Number	Words
41	Forty-One	51	Fifty-One
42	Forty-Two	52	Fifty-Two
43	Forty-Three	53	Fifty-Three
44	Forty-Four	54	Fifty-Four
45	Forty-Five	55	Fifty-Five
46	Forty-Six	56	Fifty-Six
47	Forty-Seven	57	Fifty-Seven
48	Forty-Eight	58	Fifty-Eight
49	Forty-Nine	59	Fifty-Nine
50	Fifty	60	Sixty

Number Words Chart 61 – 80

Number in figures or words are in the following table.

Number	Words	Number	Words
61	Sixty-One	71	Seventy-One
62	Sixty-Two	72	Seventy-Two
63	Sixty-Three	73	Seventy-Three
64	Sixty-Four	74	Seventy-Four
65	Sixty-Five	75	Seventy-Five
66	Sixty-Six	76	Seventy-Six
67	Sixty-Seven	77	Seventy-Seven
68	Sixty-Eight	78	Seventy-Eight
69	Sixty-Nine	79	Seventy-Nine
70	Seventy	80	Eighty

Number in Words Chart 81 – 100

Number	Words	Number	Words
81	Eighty-One	91	Ninety-One
82	Eighty-Two	92	Ninety-Two
83	Eighty-Three	93	Ninety-Three
84	Eighty-Four	94	Ninety-Four
85	Eighty-Five	95	Ninety-Five
86	Eighty-Six	96	Ninety-Six
87	Eighty-Seven	97	Ninety-Seven
88	Eighty-Eight	98	Ninety-Eight
89	Eighty-Nine	99	Ninety-Nine
90	Ninety	100	Hundred

Number Words – teen family chart

The numbers that belong to teen family are listed.

Teen Family
Number	Words
13	Thirteen
14	Fourteen
15	Fifteen
16	Sixteen
17	Seventeen
18	Eighteen
19	Nineteen

Number Words – Ty Family Chart

Numbers that are in ty – family are.

Ty Family
Number	Words
20	Twenty
30	Thirty
40	Forty
50	Fifty
60	Sixty
70	Seventy
80	Eighty
90	Ninety

Multiples of Hundred Chart

The multiples of hundreds are 100, 200, 300, 400, 500, 600, 700, 800, 900. They are expressed in words by adding prefix One, Two, Three to the word hundred such as as ‘One Hundred’, ‘Two Hundred’, ‘Three Hundred’, Four Hundred’, ‘Five Hundred’, ‘Six Hundred’, ‘Seven Hundred’, ‘Eight Hundred’, ‘Nine Hundred’.

Multiples of Hundred
100	Hundred (One Hundred)
200	Two Hundred
300	Three Hundred
400	Four Hundred
500	Five Hundred
600	Six Hundred
700	Seven Hundred
800	Eight Hundred
900	Nine Hundred

Multiples of Thousands

A thousand is basically ten hundred. It is written as 1000. Multiples of thousands have the prefix One, Two, Three and so on followed by the word thousand itself. For example, ‘One Thousand’, ‘Two Thousand’, ‘Three Thousand’, ‘Four Thousand’, ‘Five Thousand’, ‘Six Thousand’, ‘Seven Thousand’, ‘Eight Thousand’, ‘Nine Thousand’, ‘Ten Thousand’. They are listed in the following table.

Multiple of Thousands
Number	Words	Number	Words
1000	One Thousand	11000	Eleven Thousand
2000	Two Thousand	12000	Twelve Thousand
3000	Three Thousand	13000	Thirteen Thousand
4000	Four Thousand	14000	Fourteen Thousand
5000	Five Thousand	15000	Fifteen Thousand
6000	Six Thousand	16000	Sixteen Thousand
7000	Seven Thousand	17000	Seventeen Thousand
8000	Eight Thousand	18000	Eighteen Thousand
9000	Nine Thousand	19000	Nineteen Thousand
10000	Ten Thousand	20000	Twenty Thousand

Multiple of Thousands
Number	Words	Number	Words
21000	Twenty-One Thousand	31000	Thirty-One Thousand
22000	Twenty-Two Thousand	32000	Thirty-Two Thousand
23000	Twenty-Three Thousand	33000	Thirty-Three Thousand
24000	Twenty-Four Thousand	34000	Thirty-Four Thousand
25000	Twenty-Five Thousand	35000	Thirty-Five Thousand
26000	Twenty-Six Thousand	36000	Thirty-Six Thousand
27000	Twenty-Seven Thousand	37000	Thirty-Seven Thousand
28000	Twenty-Eight Thousand	38000	Thirty-Eight Thousand
29000	Twenty-Nine Thousand	39000	Thirty-Nine Thousand
30000	Thirty Thousand	40000	Forty Thousand

Multiple of Thousands
Number	Words	Number	Words
41000	Forty-One Thousand	51000	Fifty-One Thousand
42000	Forty-Two Thousand	52000	Fifty-Two Thousand
43000	Forty-Three Thousand	53000	Fifty-Three Thousand
44000	Forty-Four Thousand	54000	Fifty-Four Thousand
45000	Forty-Five Thousand	55000	Fifty-Five Thousand
46000	Forty-Six Thousand	56000	Fifty-Six Thousand
47000	Forty-Seven Thousand	57000	Fifty-Seven Thousand
48000	Forty-Eight Thousand	58000	Fifty-Eight Thousand
49000	Forty-Nine Thousand	59000	Fifty-Nine Thousand
50000	Fifty Thousand	60000	Sixty Thousand

Multiple of Thousands
Number	Words	Number	Words
61000	Sixty-One Thousand	71000	Seventy-One Thousand
62000	Sixty-Two Thousand	72000	Seventy-Two Thousand
63000	Sixty-Three Thousand	73000	Seventy-Three Thousand
64000	Sixty-Four Thousand	74000	Seventy-Four Thousand
65000	Sixty-Five Thousand	75000	Seventy-Five Thousand
66000	Sixty-Six Thousand	76000	Seventy-Six Thousand
67000	Sixty-Seven Thousand	77000	Seventy-Seven Thousand
68000	Sixty-Eight Thousand	78000	Seventy-Eight Thousand
69000	Sixty-Nine Thousand	79000	Seventy-Nine Thousand
70000	Seventy Thousand	80000	Eighty Thousand

Multiple of Thousands
Number	Words	Number	Words
81000	Eighty-One Thousand	91000	Ninety-One Thousand
82000	Eighty-Two Thousand	92000	Ninety-Two Thousand
83000	Eighty-Three Thousand	93000	Ninety-Three Thousand
84000	Eighty-Four Thousand	94000	Ninety-Four Thousand
85000	Eighty-Five Thousand	95000	Ninety-Five Thousand
86000	Eighty-Six Thousand	96000	Ninety-Six Thousand
87000	Eighty-Seven Thousand	97000	Ninety-Seven Thousand
88000	Eighty-Eight Thousand	98000	Ninety-Eight Thousand
89000	Eighty-Nine Thousand	99000	Ninety-Nine Thousand
90000	Ninety Thousand	1,000,000	One-Hundred Thousand

Example No. 1

Write the number 24 + 56 – 6 in words.

Solution

To write the number in words, we must solve the given expression first.

24 + 56 – 6

Using DMAS (Division-Multiplication-Addition-Subtraction) Rule.

Now the expression becomes, 80 – 6. We can do subtraction by regrouping. Since in unit column the minuend (0) is smaller than the subtrahend (6), we must regroup and borrow one (1) from the ten column such that the minuend of unit column become 10. Now 10 – 6 = 4.

In the ten column it is 7 – 0 which gives 7. So, the difference of 80 – 6 is 74.

To write 74 in words, we can write four for 4 preceded by the prefix seventy for 7 in tens place.

74	Seventy-Four

Example No. 2

Simplify the expression and write in words the value of expression i.e., 71 + 19 – (67 + 11)

Solution

To simplify this expression, we first solve the brackets i.e., 67 + 11.

Since 67 + 11 = 78, the expression simplifies to 71 + 19 – 78. We will use DMAS (Division-Multiplication-Addition-Subtraction) rule from here onwards.

Since 71 + 19 = 90, the expression simplifies to 90 – 78. In subtraction, we will be doing regrouping because in unit column minuend is less than subtrahend. When we borrow one (1) from tens column, the minuend in unit column becomes 10. So, 10 – 8 is 2. We can write it below the unit column.

In tens column it is not 9 but 8 (due to regrouping), so 8 – 7 is 1. The answer is 12.

We can write this in words by applying rule number 2.

12

Twelve

Example No. 3

How to write 8,452,956,752,821 in words using international system of numbering.

Answer

In international system of numbering, the columns from right to left are.

• Unit
• Tens
• Hundred
• Thousand
• Ten thousand
• Hundred Thousand
• Million
• Ten Million
• Hundred Million
• Billion
• Ten Billion
• Hundred Billion
• Trillion

Since, we have thirteen (13) columns, so we will go up to trillion only. The number can be written in words as.

8,452,956,752,821

Eight trillion, four hundred and fifty-two billion, nine hundred and fifty-six million, seven hundred and fifty-two thousand, eight hundred and twenty-one.

Example No. 4

How to write 84,52,95,67,52,821 in words using Indian system of numbering.

Answer

In Indian system of numbering, the columns from right to left are.

• Unit
• Tens
• Hundred
• Thousand
• Ten Thousand
• Lakh
• Ten Lakh
• Crore
• Ten Crore
• Arab
• Ten Arab
• Kharab
• Ten Kharab

Since, we have thirteen (13) columns, so we will go up to trillion only. The number can be written in words as.

84,52,95,67,52,821

Eighty-four Kharab, fifty-two Arabs, ninety-five crores, sixty-seven lakhs, fifty-two thousand, eight hundred and twenty-one.

References

[1]	“BYJU’S,” BYJU’S, 2021. [Online]. Available: https://byjus.com/maths/numbers-in-words/. [Accessed 21 9 2021].
[2]	“CUEMATH,” CUEMATH, 2021. [Online]. Available: https://www.cuemath.com/numbers/number-names/. [Accessed 22 9 2021].
[3]	W. L. Hosch, “The Arabic Numeral System.,” Hindu-Arabic numerals, p. 1, 8 9 2017.
[4]	C. Brezina, “A Scholar of Baghdad,” in Al-Khwarizmi: The Inventor of Algebra, New York, The Rosen publishing Group, Inc, 2006, pp. 39-40.
[5]	“Prezi,” Prezi Inc., 2021. [Online]. Available: https://prezi.com/qrs6rqz7eliw/why-do-we-use-numbers/. [Accessed 24 9 2021].