Big numbers all around us

Picture the Narendra Modi Stadium in Ahmedabad on the day of a big cricket final. Every seat is full: about 1,32,000 people are cheering. Now picture every one of those fans holding up a card with a number on it, and the numbers go 1, 2, 3, … all the way to the last fan. How would you say that last number? How would you write it so that someone else can read it at a glance?

Numbers like this are everywhere in India. A train carries more than a thousand passengers. A new car costs several lakh rupees. India's 2011 census counted 1,21,08,54,977 people. This lesson is about how we manage to write all of these with just ten little symbols, 0 to 9.

Small numbers are easy: you can see 3 mangoes or 7 pencils at once. But once numbers grow past a few hundred, nobody can picture them directly. So people invented a system: a set of rules for writing numbers so that even huge ones can be read, compared and calculated with.

Here are some real Indian numbers you will be able to read by the end of this lesson. Do not worry if they look scary now.

Every number you have ever written uses only these ten digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. There is no special symbol for ten, or for a hundred, or for a crore. So how do we write ten? We write 10: a 1 and a 0. The trick is where the digit sits.

Think of bundling sticks. Count out loose sticks. When you reach ten, tie them into one bundle. Now you have 1 bundle and 0 loose sticks, and that is exactly what 10 means. Keep going: when you have ten bundles, tie them into one big bundle of a hundred. The number 347 means 3 big bundles, 4 bundles and 7 loose sticks.

Each place is ten times the place on its right. Going right to left, the places are ones, tens, hundreds, thousands, ten thousands, and then… the names depend on whether you use the Indian system or the International system. We will meet both. For now, here are the first five places, which are the same everywhere.

The number of digits tells you roughly how big a number is. Every 2-digit number is at least 10, every 3-digit number is at least 100 and every 4-digit number is at least 1,000. So a 4-digit number is always bigger than any 3-digit number, however large its digits are: 1,000 is more than 999.

Add up the four place values in the table: 5,000 + 500 + 50 + 5 = 5,555. That is no accident. A number is always the sum of the place values of its digits. Writing a number this way, as a sum, is called its expanded form.

What comes after 99,999? Add one more and every 9 rolls over to 0, just like a car's odometer: 99,999 + 1 = 1,00,000. In India we call this number one lakh. It is a hundred thousand.

Keep going. Ten lakh is 10,00,000. A hundred lakh gets a new name: one crore, written 1,00,00,000. So in the Indian system, the places after ten thousands are lakhs, ten lakhs, crores, ten crores.

Look at how the chart is split into periods. The ones period has three places (hundreds, tens, ones). Every period after that has just two places. Commas separate the periods, so an Indian number gets its first comma after 3 digits from the right, and then a comma after every 2 digits.

So 12345678 is written 1,23,45,678 and read one crore twenty-three lakh forty-five thousand six hundred seventy-eight. Each comma tells you the name to say: crore, lakh, thousand.

Most of the world groups digits in threes, all the way. After thousands and ten thousands comes hundred thousands, and then a new period: millions. A thousand thousands make a million, 1,000,000. A thousand millions make a billion, 1,000,000,000.

So in the International system the periods are ones, thousands, millions, billions, and every period has three places. The commas go after every three digits from the right: 12345678 is written 12,345,678 and read twelve million three hundred forty-five thousand six hundred seventy-eight.

Why bother with commas at all? Try reading 100000000 quickly. Now try 10,00,00,000. The commas chop a long row of digits into small groups your eyes can count at a glance, and each comma is a signpost that tells you which name to say next. Both systems do the same job; they just put the signposts in different places.

To read a big number, read it one period at a time, from the left, and say the period's name at each comma. Periods that are all zeros are skipped.

• Indian: 4,05,00,309 → four crore | five lakh | (no thousands) | three hundred nine.
• International: 40,500,309 → forty million | five hundred thousand | three hundred nine.

In number names we say lakh, crore and million without an s: five lakh, not five lakhs. (When we name a place, like the lakhs place, we do use the plural.)

The number that comes just after a number is its successor: add 1. The number that comes just before is its predecessor: subtract 1.

• The successor of 4,599 is 4,600.
• The predecessor of 4,600 is 4,599.
• The predecessor of 1 is 0. Among whole numbers, 0 has no predecessor.

Watch out when a number ends in 9s or 0s: adding or taking away 1 can change several digits at once, like a car's odometer rolling over.

Often we do not need an exact number. "About 1,30,000 people watched the final" is easier to remember than 1,32,014. Choosing a nearby, simpler number is called rounding.

To round 47 to the nearest ten, ask: is 47 closer to 40 or to 50? It is 7 away from 40 and 3 away from 50, so it rounds to 50. A number exactly in the middle, like 45, is rounded up to 50 by the usual school rule.

Look at an old clock face, or the chapter numbers in some books, or "Class VI" on a school notebook. These are Roman numerals, used in ancient Rome about 2,000 years ago. They use letters instead of digits.

The rules are simple to start with:

• Add symbols written from biggest to smallest: VI = 5 + 1 = 6, XXV = 10 + 10 + 5 = 25, CLX = 100 + 50 + 10 = 160.
• Subtract a smaller symbol written just before a bigger one: IV = 5 − 1 = 4, IX = 10 − 1 = 9, XL = 50 − 10 = 40.
• A symbol is not repeated more than three times: 3 is III, but 4 is IV, not IIII.

So the classes at school are I, II, III, IV, V, VI, VII, VIII, IX, X. And this year, 2026, is MMXXVI.