Crores and millions: one number, two naming systems

0:00Here is a button. Every time you press it, it adds ten lakh. Ten lakh is a one with six zeros after it. Press it once and the screen shows ten lakh. Press it twice, twenty lakh. Keep pressing. Fifty lakh. Eighty lakh. Ninety lakh. Press it a tenth time, and the screen shows a hundred lakh. That quantity has a name of its own. A hundred lakh is one crore.

0:27Written out, a crore is a one followed by seven zeros. And that is where this starts, because a crore is about to meet a word that looks like its twin and is not. Here is a string of digits. Nine, eight, seven, six, five, zero, one, two, three, four. Ten digits in a row, and almost impossible to read. That is what commas are for. They cut the digits into groups, and each group takes a name.

0:58But there are two different ways to make the cuts, and both of them are correct. The first way puts a comma after three digits from the right, and then after every two. The second way puts a comma after every three digits, all the way along. Same digits. Same number. Two different sets of cuts. And once the cuts land in different places, the groups pick up completely different names.

1:28Let's put the two rules side by side. The Indian system: three, then two, then two, then two. The American system, which is also called the international system: three, three, three. Notice where they agree. Both put the first comma after three digits from the right. That is the thousands comma, and it is in the same place either way. After that they part company completely. And it is worth saying what this is not. The Indian commas are not the American ones shifted along.

2:04It is a different rule. Three and then twos, against threes the whole way. Now watch what those cuts do to the names. A thousand is a thousand in both. Ten thousand is ten thousand in both. Add one more zero and they split apart. One side calls it a lakh. The other calls it a hundred thousand. Another zero. Ten lakh here. A million there. Another. One crore, against ten million.

2:36Another. Ten crore, against a hundred million. And one more. One arab, which is also a hundred crore, against one billion. Now look down the middle of that ladder. The digits are identical on every single row. Nothing about the number changed. Only where we cut it, and what we called the pieces. So let's get the sizes straight by counting zeros. A lakh is a one with five zeros.

3:07A million is a one with six. A crore is a one with seven. An arab is a one with nine, and so is a billion. Those two are the same size. Five, six, seven, nine. Those four counts settle almost every question in this topic. Here is one immediately. How many zeros are there in a thousand lakh? A lakh has five. A thousand of anything adds three more. Eight zeros.

3:37And a hundred thousand? Five zeros. Which means a hundred thousand is exactly one lakh. There is a pattern hiding in those zero counts, and it runs differently on each side. Climb the Indian ladder. Thousand, lakh, crore, arab. A lakh is a hundred thousands. A crore is a hundred lakhs. An arab is a hundred crores. A hundred times, at every single step. Now climb the other one. Thousand, million, billion.

4:12A million is a thousand thousands. A billion is a thousand millions. A thousand times, at every step. Two ladders up the same wall, with the rungs at different heights. That is the entire reason the names never line up, and every confusion in this topic comes out of it. Let's read a real number out loud, twice over. Nine, eight, seven, six, five, zero, one, two, three, four. Cut it the Indian way, and the groups are nine, eighty seven, sixty five, zero one, and two three four.

4:51Read them off: nine arab, eighty seven crore, sixty five lakh, one thousand, two hundred and thirty four. You can also say it without the arab. Nine hundred and eighty seven crore, sixty five lakh, one thousand, two hundred and thirty four. Same number. Now cut those same digits the other way. The groups are nine, then eight seven six, then five zero one, then two three four. Read them off: nine billion, eight hundred and seventy six million, five hundred and one thousand, two hundred and thirty four.

5:29Two completely different sentences, and not one digit moved. So where do these names come from? Lakh and crore come from Sanskrit, and they are not used only in India. The same system is used right across the region. Nepal and Bhutan, Bangladesh and Myanmar, Sri Lanka and the Maldives, Pakistan and Afghanistan. Millions and billions are used across a great many countries too, which is why that system also gets called the international one.

6:05Neither of them is more correct than the other. They are two conventions for cutting up the same digits. The digits are the number; the commas are punctuation. But punctuation starts to matter the moment you try to compare two quantities that were named in different places. So here is the skill that actually matters. Which is bigger: five hundred lakh, or five million? The names give you no help at all. Five hundred certainly sounds bigger than five.

6:40So do not compare the names. Convert both to plain digits first. Five hundred lakh is five crore, which is a five with seven zeros. Five million is a five with six zeros, which is fifty lakh. Five crore against fifty lakh. The first one is ten times the second. Convert, then compare. Never compare the labels. Which brings us to the two mistakes that do the most damage. The first one is treating a lakh as the Indian word for a million.

7:16It is not. A million is ten lakh. They are a factor of ten apart. The second is treating a crore as the Indian word for a billion. Also wrong, and wrong by more. A billion is a hundred crore. A crore is ten million. If you want the true partners, here they are. A million sits opposite ten lakh. A billion sits opposite one arab. Those pairings are exact. Lakh and million are not a pair, and crore and billion are not a pair.

7:49Fifty lakh and five million, on the other hand, are the same crowd of people. One last thing, about the top of the ladder. We stopped at arab and billion, and that is not because numbers stop there. Both systems carry on upwards with more names, and those come later. What does not change is the idea underneath all of it. A number is a run of digits. The commas are a reading aid, and different places read them differently.

8:23So whenever you meet one quantity named one way and another named the other way, do the same three things. Write both in digits. Line up the zeros. Then compare. Here is a question to leave you with. How many lakh are there in one billion? You have everything you need. A billion is a one with nine zeros, and a lakh is a one with five. Work that out. Then say the size of a crowd of ten million people twice, once in each system.