Lakhs and crores: reading and writing large numbers

From thousands to a lakh

You already know 5-digit numbers such as 45,830. The largest of them is 99,999. Add 1 and every 9 turns into 0 with a carry, giving 1,00,000, a 6-digit number we call one lakh. Written in figures, it is 1 followed by 5 zeros.

A lakh is a hundred thousands. You can see this on the one-key calculators of the Land of Tens: a calculator that only adds 1000 needs 100 presses to reach a lakh, one that adds 100 needs 1,000 presses, and one that adds 10 needs 10,000 presses.

Commas in the Indian system

Commas make big numbers easy to read. In the Indian place value system, count three digits from the right and put a comma, then put a comma after every two digits: 34,56,789. Each group has a name. The last three digits are the ones group (hundreds, tens, ones); then come thousands, lakhs and crores. So 34,56,789 is read as thirty-four lakh fifty-six thousand seven hundred eighty-nine.

To write a number from its name, fill each group and put zeros in the empty places. Fifty lakh five thousand fifty is 50,05,050, and ten lakh two hundred thirty-five is 10,00,235.

Crore and arab

Ten lots of 10 lakh make 100 lakh, which is called a crore: 1,00,00,000, with 7 zeros. A hundred crore make an arab, 1,00,00,00,000, with 9 zeros. Each step up is 100 times bigger: thousand, lakh, crore, arab. A thousand lakh is 10 crore and has 8 zeros. The word lakh comes from the Sanskrit laksha and crore from koti. The Indian system is also used in several neighbouring countries, such as Nepal, Bangladesh and Sri Lanka.

The American system

Many countries use the American, or International, system. It puts a comma after every three digits from the right, and its names change every three places: thousand, million, billion. A million is 1,000,000 and a billion is 1,000,000,000.

The same number can be written both ways. 9876501234 becomes 9,87,65,01,234 in the Indian system, read as 9 arab 87 crore 65 lakh 1 thousand 234, and 9,876,501,234 in the American system, read as 9 billion 876 million 501 thousand 234. The digits never change; only the grouping and the names do.

Changing from one system to the other

A few facts are enough for most conversions:

• 1 lakh = 100 thousand
• 10 lakh = 1 million
• 1 crore = 10 million
• 100 crore = 1 arab = 1 billion
• 10,000 lakh = 1 billion

So 3 crore is 30 million, 750 crore is 7.5 billion, and 25 lakh is two and a half million. To compare 640 crore with 60 billion, change both to crores: 60 billion is 6,000 crore, so 640 crore is smaller.

Place value and the fewest clicks

A calculator with the keys +1, +10, +100, +1000 and so on can make 5072 in many ways, for example 50 clicks of +100, 7 of +10 and 2 of +1. The fewest clicks come from pressing each key at most 9 times: 5 of +1000, 7 of +10 and 2 of +1, which is 14 clicks, the sum of the digits. That is no accident. Ten clicks on one key can always be swapped for one click on the next key, so the smallest set of clicks is exactly the digits of the number, place by place.

Why it matters

News reports, budgets and census figures use lakhs and crores in India and millions and billions elsewhere, so it helps to move easily between them. Practise rounding such numbers in rounding and estimation, and try multiplying them in patterns in products. Every textbook question is answered in the NCERT solutions for Chapter 1; see all of the Chapter 1 notes.