International Number System
In the international number system you group digits in threes and put a comma after each group. Learn the place value chart from ones to billions, how to read and write large numbers in words, and how it compares with lakh and crore.
The international number system writes a large number by grouping its digits in threes from the right and putting a comma after each group. The groups are called periods: ones, thousands, millions and billions. So 1234567890 is written 1,234,567,890 and read “one billion, two hundred thirty-four million, five hundred sixty-seven thousand, eight hundred ninety.” The same system is also called the international counting system or the international system of numeration.
This page gives you the place value chart up to billions, shows where the commas go and how to read and write numbers in words. Then it compares the system with the Indian system (lakh and crore) and covers expanded form, ordering and rounding. The digits themselves are explained on the Hindu-Arabic numerals page, and other bases such as binary are on number systems.
International place value chart: ones to billions
Every place is worth ten times the place to its right. In the international system the places are collected in groups of three, called periods. Each period has a hundreds, a tens and a ones place, and only the period name changes. The chart shows 123,456,789,012 with all twelve places.
| Billions | Millions | Thousands | Ones | ||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| H | T | O | H | T | O | H | T | O | H | T | O |
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 0 | 1 | 2 |
| one hundred twenty-three billion | four hundred fifty-six million | seven hundred eighty-nine thousand | twelve | ||||||||
The next table lists every place with its value, from ones up to hundred billions.
| Place | Period | Value | Power of ten |
|---|---|---|---|
| ones | Ones | 1 | 100 |
| tens | Ones | 10 | 101 |
| hundreds | Ones | 100 | 102 |
| thousands | Thousands | 1,000 | 103 |
| ten thousands | Thousands | 10,000 | 104 |
| hundred thousands | Thousands | 100,000 | 105 |
| millions | Millions | 1,000,000 | 106 |
| ten millions | Millions | 10,000,000 | 107 |
| hundred millions | Millions | 100,000,000 | 108 |
| billions | Billions | 1,000,000,000 | 109 |
| ten billions | Billions | 10,000,000,000 | 1010 |
| hundred billions | Billions | 100,000,000,000 | 1011 |
Reading the periods
To read a number, start at the left. Say the three-digit number of each period and then the period name. The ones period has no name. A period of 000 is skipped completely: 5,000,200 is “five million, two hundred,” not “five million, zero thousand, two hundred.”
How to put commas in a number
- Start at the right end of the whole number, before any decimal point.
- Count three digits to the left and put a comma there.
- Repeat until fewer than four digits are left.
So 5628937 becomes 5,628,937, 40050000 becomes 40,050,000 and 1234567.891 becomes 1,234,567.891, because digits after the decimal point are not grouped. Most books write four-digit numbers with a comma (1,000), some without (1000). Years such as 2026, page numbers and phone numbers never get commas.
International number system in words: reading and writing numbers
Split the number into periods, read each period as a three-digit number and add the period name. Use a hyphen for 21 to 99, as in forty-two. American English leaves out “and” in whole numbers: “one hundred twenty-three.” Indian and British books usually add it after the hundreds: “one hundred and twenty-three.” Follow your textbook.
| Number | In words |
|---|---|
| 4,205 | four thousand, two hundred five |
| 56,018 | fifty-six thousand, eighteen |
| 300,070 | three hundred thousand, seventy |
| 2,040,506 | two million, forty thousand, five hundred six |
| 70,000,009 | seventy million, nine |
| 123,456,789 | one hundred twenty-three million, four hundred fifty-six thousand, seven hundred eighty-nine |
| 5,006,000,300 | five billion, six million, three hundred |
| 80,500,000,000 | eighty billion, five hundred million |
| 123,456,789,012 | one hundred twenty-three billion, four hundred fifty-six million, seven hundred eighty-nine thousand, twelve |
Indian and international number system compared
The Indian system uses the same ten digits and the same place values, but it groups them differently. The last three digits form the first group, and every group after that has two digits. So 123,456,789 is written 12,34,56,789 in India. The names are thousand, lakh (100,000), crore (10,000,000), arab (100 crore) and kharab (100 arab). It is used in India, Pakistan, Bangladesh, Nepal and Sri Lanka, while the international system is used in the United States, the United Kingdom and most other countries. Indian school mathematics teaches both and asks you to convert between them.
| Indian unit | Indian grouping | International grouping | International words |
|---|---|---|---|
| 1 lakh | 1,00,000 | 100,000 | one hundred thousand |
| 10 lakh | 10,00,000 | 1,000,000 | one million |
| 1 crore | 1,00,00,000 | 10,000,000 | ten million |
| 10 crore | 10,00,00,000 | 100,000,000 | one hundred million |
| 100 crore (1 arab) | 1,00,00,00,000 | 1,000,000,000 | one billion |
| 1 lakh crore (10 kharab) | 10,00,00,00,00,000 | 1,000,000,000,000 | one trillion |
Up to 99,999 both systems look the same. From 100,000 on they differ:
| International | Indian | Read in the Indian system |
|---|---|---|
| 750,000 | 7,50,000 | seven lakh, fifty thousand |
| 1,234,567 | 12,34,567 | twelve lakh, thirty-four thousand, five hundred sixty-seven |
| 25,000,000 | 2,50,00,000 | two crore, fifty lakh |
| 987,654,321 | 98,76,54,321 | ninety-eight crore, seventy-six lakh, fifty-four thousand, three hundred twenty-one |
| 1,500,000,000 | 1,50,00,00,000 | one arab, fifty crore |
Converting between the Indian and the international system
The digits never change, only the commas. Remove all commas, then put them back with the other rule. For amounts, the units are faster: divide lakh by 10 to get millions (45 lakh = 4.5 million), multiply crore by 10 to get millions (3.5 crore = 35 million), and divide crore by 100 to get billions (250 crore = 2.5 billion).
Billion in other languages: short scale and long scale
The international system as used in English follows the short scale: a new name appears every factor of 1,000, so a billion has 9 zeros. Many languages of continental Europe follow the long scale, where a new name appears every factor of 1,000,000. British English used to follow the long scale too, so a billion meant 1012. Official UK statistics have used the short scale since 1974. The Indian words do not have this problem: 1 arab is always 1,000,000,000.
| Power | Number | English (short scale) | German (long scale) | French (long scale) |
|---|---|---|---|---|
| 106 | 1,000,000 | million | Million | million |
| 109 | 1,000,000,000 | billion | Milliarde | milliard |
| 1012 | 1,000,000,000,000 | trillion | Billion | billion |
| 1015 | 1,000,000,000,000,000 | quadrillion | Billiarde | billiard |
| 1018 | 1,000,000,000,000,000,000 | quintillion | Trillion | trillion |
Expanded form and the value of a digit
The expanded form writes a number as the sum of the values of its digits. Places with a zero are left out. The face value of a digit is the digit itself, and its place value is the digit times the value of its place.
The same digit can have several place values in one number. In 5,250,500 the digit 5 is worth 5,000,000, 50,000 and 500.
Comparing and ordering large numbers
- The number with more digits is greater: 12,345,678 > 9,876,543.
- With the same number of digits, compare from the left. The first digit that differs decides: 4,375,201 > 4,375,120, because 2 hundreds are more than 1 hundred.
To order numbers, sort by the number of digits first, then compare from the left. Ascending order of 52,408,100, 5,240,810, 52,410,008 and 52,408,010 is 5,240,810 < 52,408,010 < 52,408,100 < 52,410,008. Descending order is 52,410,008 > 52,408,100 > 52,408,010 > 5,240,810.
To make the greatest number from digits, put the largest digit first. The digits 3, 0, 7, 5, 9, 1, each used once, give 975,310 as the greatest and 103,579 as the smallest 6-digit number. The smallest cannot start with 0.
Rounding large numbers
To round to a place, look at the digit directly to its right. If it is 0 to 4, keep the digit and replace everything to its right with zeros. If it is 5 to 9, add 1 to the digit first.
| Round to the | Digit to look at | Result |
|---|---|---|
| nearest thousand | 6 | 3,482,000 |
| nearest ten thousand | 1 | 3,480,000 |
| nearest hundred thousand | 8 | 3,500,000 |
| nearest million | 4 | 3,000,000 |
Rounding helps with estimates: 3,481,672 + 2,519,804 is about 3,500,000 + 2,500,000 = 6,000,000 after rounding both to the nearest hundred thousand. The exact sum is 6,001,476.
Common mistakes
Practice problems with answers
Frequently asked questions
What is the international number system?
It is the way of writing and naming numbers in which digits are grouped in threes from the right, with a comma after each group. The groups are ones, thousands, millions and billions. See the place value chart.
What is the difference between the Indian and the international number system?
The international system groups all digits in threes (1,234,567) and uses million and billion. The Indian system groups the last three digits and then pairs (12,34,567) and uses lakh and crore. The digits and place values are the same. See the comparison.
What is an example of the international number system?
123,456,789 is read “one hundred twenty-three million, four hundred fifty-six thousand, seven hundred eighty-nine.” The commas separate the millions, thousands and ones periods.
How many zeros are in a million, a billion and a trillion?
A million has 6 zeros, a billion 9 and a trillion 12. In the Indian system a lakh has 5 zeros and a crore 7.
How many lakh make a million, and how many crore make a billion?
10 lakh make a million, and 100 crore make a billion. One crore is 10 million. See the conversion table.
Is a billion the same everywhere?
No. In English it is 1,000,000,000. In German and French, which use the long scale, Billion or billion means 1,000,000,000,000. See short scale and long scale.
What are the units, tens, hundreds and thousands places?
They are the first four places from the right: ones (units) 1, tens 10, hundreds 100 and thousands 1,000. In 4,205 there are 4 thousands, 2 hundreds, 0 tens and 5 units. See the place value chart.
What is the American, British or English number system?
All three use the international system with the short scale: commas every three digits and a billion of 1,000,000,000. Americans leave out “and” in words (one hundred twenty-three), British writers usually add it. See numbers in words.
How do you write sixteen thousand and other numbers from words in figures?
Sixteen thousand is 16,000. Write the number before each period name in its place and fill empty places with zeros: “two million, five” is 2,000,005.
Why do we put commas in large numbers?
They make long numbers easy to read, and they mark the periods. The names repeat every three places, so a comma every three digits shows you where to say thousand, million or billion.
Sources and further reading
- NCERT: Exemplar Problems, Mathematics Class VI, Unit 1 Number System (covers the Indian and the international system)
- NIST Guide for the Use of the International System of Units (SI), Chapter 10: grouping digits
- NIST: Metric (SI) prefixes
- Encyclopaedia Britannica: Numeral system
- Wikipedia: Indian numbering system and Long and short scales
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