Why Indians Say Lakh and Everyone Else Says Million
Learn to read and write nine-digit numbers in both the Indian and International systems, place the commas correctly, and convert between lakhs, crores and millions.
What is the difference between the Indian and International systems?
Both systems write the same number using the same digits — they only group those digits differently. The Indian system groups into ones, thousands, lakhs and crores; the International system groups into ones, thousands, millions and billions. So one number can be read aloud two different ways without changing its value at all.
This page covers everything in the ICSE Class 6 Mathematics chapter on place value and the two number systems: where the commas go, how place value differs from face value, how to build the greatest and smallest numbers from given digits, and how to convert between lakhs and millions.
This page covers everything in the ICSE Class 6 Mathematics chapter on place value and the two number systems: where the commas go, how place value differs from face value, how to build the greatest and smallest numbers from given digits, and how to convert between lakhs and millions.
Where exactly do the commas go in a large number?
Commas exist to break a long string of digits into readable groups called periods, and the two systems place them differently.
In the Indian system, you place a comma after the first three digits from the right, and then after every two digits. So 428657391 becomes 42,86,57,391 and is read as forty-two crore eighty-six lakh fifty-seven thousand three hundred ninety-one.
In the International system, you place a comma after every three digits from the right. The same number becomes 428,657,391 and is read as four hundred twenty-eight million six hundred fifty-seven thousand three hundred ninety-one.
For example, a news report about a city's population might print 1,25,00,000 in an Indian newspaper and 12,500,000 in an international one. Both mean one crore twenty-five lakh, which is also twelve and a half million.
The usual slip is starting from the left. Always count from the right, because the rightmost digit is the ones place and the grouping is built outward from there.
In the Indian system, you place a comma after the first three digits from the right, and then after every two digits. So 428657391 becomes 42,86,57,391 and is read as forty-two crore eighty-six lakh fifty-seven thousand three hundred ninety-one.
In the International system, you place a comma after every three digits from the right. The same number becomes 428,657,391 and is read as four hundred twenty-eight million six hundred fifty-seven thousand three hundred ninety-one.
For example, a news report about a city's population might print 1,25,00,000 in an Indian newspaper and 12,500,000 in an international one. Both mean one crore twenty-five lakh, which is also twelve and a half million.
The usual slip is starting from the left. Always count from the right, because the rightmost digit is the ones place and the grouping is built outward from there.
What is the difference between place value and face value?
The face value of a digit is simply the digit itself, wherever it sits. The place value of a digit is the digit multiplied by the value of the position it occupies.
Take the number 5,74,206 and look at the digit 7. Its face value is just 7. But it sits in the ten thousands place, so its place value is .
The expanded form writes a number as the sum of the place values of all its digits:
Notice that the digit 0 in the tens place contributes nothing to the total, yet it cannot be removed — it holds the other digits in their correct positions. Delete it and 574206 collapses into 57426, a completely different number.
For example, in a price of Rs 4,32,000 the digit 4 has a face value of 4 but a place value of rupees — which is most of the price.
Take the number 5,74,206 and look at the digit 7. Its face value is just 7. But it sits in the ten thousands place, so its place value is .
The expanded form writes a number as the sum of the place values of all its digits:
Notice that the digit 0 in the tens place contributes nothing to the total, yet it cannot be removed — it holds the other digits in their correct positions. Delete it and 574206 collapses into 57426, a completely different number.
For example, in a price of Rs 4,32,000 the digit 4 has a face value of 4 but a place value of rupees — which is most of the price.
How do you make the greatest and smallest numbers from given digits?
To build the greatest number, put the digits in descending order, so the largest digit occupies the highest place. To build the smallest, put them in ascending order.
Using the digits 7, 2, 9, 4 without repeating any:
- greatest: 9742
- smallest: 2479
There is one trap. If 0 is among the digits, it cannot go first, because a leading zero is not written. With 0, 5, 3, 8 the smallest number is 3058, not 0358 — you place the smallest non-zero digit first, then the 0, then the rest in ascending order.
When repetition is allowed, the greatest four-digit number from 6, 1 is 6666 and the smallest is 1111.
To arrange numbers in ascending or descending order, first compare how many digits each has; a number with more digits is always larger. Only when the digit counts match do you compare from the leftmost digit onwards.
Using the digits 7, 2, 9, 4 without repeating any:
- greatest: 9742
- smallest: 2479
There is one trap. If 0 is among the digits, it cannot go first, because a leading zero is not written. With 0, 5, 3, 8 the smallest number is 3058, not 0358 — you place the smallest non-zero digit first, then the 0, then the rest in ascending order.
When repetition is allowed, the greatest four-digit number from 6, 1 is 6666 and the smallest is 1111.
To arrange numbers in ascending or descending order, first compare how many digits each has; a number with more digits is always larger. Only when the digit counts match do you compare from the leftmost digit onwards.
Formula
How do you convert lakhs and crores into millions and billions?
The conversions follow from the number of zeros in each unit:
Comparing these gives the two rules you actually use:
Worked example: convert 8 crore into millions. Since 1 crore is 10 million,
Worked example the other way: convert 250 million into crores. Since 10 million make 1 crore,
To compare two numbers written in different systems, convert both to plain digits first. Is 9 crore larger than 85 million? Write them out: 90000000 against 85000000. Yes, 9 crore is larger.
Comparing these gives the two rules you actually use:
Worked example: convert 8 crore into millions. Since 1 crore is 10 million,
Worked example the other way: convert 250 million into crores. Since 10 million make 1 crore,
To compare two numbers written in different systems, convert both to plain digits first. Is 9 crore larger than 85 million? Write them out: 90000000 against 85000000. Yes, 9 crore is larger.
Exam tip
The mistake most students make with comma placement
Students often apply the Indian grouping but then read the number using International names, producing answers like "forty-two million eighty-six lakh" — a mixture that means nothing.
Pick one system and stay in it for the whole answer. If the question shows 42,86,57,391 with Indian commas, answer in crore and lakh. If it shows 428,657,391, answer in million.
A quick self-check: in the Indian system the leftmost group can have one or two digits, and every group except the rightmost has exactly two. In the International system every group except the rightmost has exactly three. If your commas do not fit one of those patterns, they are wrong.
Pick one system and stay in it for the whole answer. If the question shows 42,86,57,391 with Indian commas, answer in crore and lakh. If it shows 428,657,391, answer in million.
A quick self-check: in the Indian system the leftmost group can have one or two digits, and every group except the rightmost has exactly two. In the International system every group except the rightmost has exactly three. If your commas do not fit one of those patterns, they are wrong.
Did you know
Why is a lakh written with five zeros and not six?
The Indian system counts in steps of one hundred after the thousands place — a lakh is a hundred thousand, and a crore is a hundred lakh. The International system keeps stepping in thousands throughout, so a million is a thousand thousand and a billion is a thousand million.
That single difference in step size is the whole reason the two systems drift apart, and why ten lakh, not one lakh, matches a million.
That single difference in step size is the whole reason the two systems drift apart, and why ten lakh, not one lakh, matches a million.
Key takeaways
Place value in 30 seconds
- The Indian system groups digits into ones, thousands, lakhs and crores; the International system into ones, thousands, millions and billions.
- Commas are counted from the right: 3 then 2-at-a-time for Indian, 3-at-a-time for International.
- Face value is the digit itself; place value is the digit multiplied by its position value, and the expanded form adds all the place values together.
- Descending digits give the greatest number and ascending digits the smallest, except that 0 may never be placed first.
- 10 lakh = 1 million and 1 crore = 10 million; convert both numbers to plain digits before comparing across systems.
You will remember all of this far better after answering five questions on it than after reading it twice.
- Commas are counted from the right: 3 then 2-at-a-time for Indian, 3-at-a-time for International.
- Face value is the digit itself; place value is the digit multiplied by its position value, and the expanded form adds all the place values together.
- Descending digits give the greatest number and ascending digits the smallest, except that 0 may never be placed first.
- 10 lakh = 1 million and 1 crore = 10 million; convert both numbers to plain digits before comparing across systems.
You will remember all of this far better after answering five questions on it than after reading it twice.