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Unit 1 · Topic 01 · Number System & Notation

Indian vs International Number System

Hook

Anaya's cricket app said the stadium had 1,25,000 seats. Her cousin in London opened the same app and it said 125,000.

Same stadium. Same seats. The commas had moved.

Anaya was sure one of them had a broken app.

Watch the Lesson

The Story

Ms. Rao drew a place-value table on the board: Ones, Tens, Hundreds, Thousands, Ten Thousands, Lakhs, Ten Lakhs, and so on.

"A period is a group of place values," she said. "In the Indian system we read in three main periods: thousands, lakhs, and crores. Commas show where each period begins."

She wrote digits into the table: 5 in lakhs, 2 in ten lakhs, 7 in thousands, 8 in ten thousands, 6 in hundreds, 4 in tens, 1 in ones.

"Read it aloud," she said. Anaya tried: "Fifty-two lakh, seventy-eight thousand, six hundred forty-one."

Ms. Rao added commas: 52,78,641. "After the ones period take three digits, then comma. In thousands take two digits, then comma. In lakhs take two digits, then comma if more periods follow."

Kabir tried the next example: 8,24,05,936. "Eight crore, twenty-four lakh, five thousand, nine hundred thirty-six."

Then 40,30,80,207: "Forty crore, thirty lakh, eighty thousand, two hundred seven."

Anaya's cousin Veer wrote the same digits the International way — commas every three from the right: 403,080,207. Same digits, different grouping names, but the stadium seat count had never changed.

"Periods are for reading and writing," said Ms. Rao. "The digits stay fixed. Only the commas and the words we use to read them change with the system."

The same six digits grouped two different waysAnaya's screen (Indian)1,25,000one lakh twenty-five thousandVeer's screen (International)125,000one hundred twenty-five thousand
The digits are identical on both lines. Only the commas moved.

So What Just Happened?

In the Indian system, a period is a group of place values. The main periods are ones (three places from the right), thousands (two places), lakhs (two places), and crores (two places).

Commas mark period boundaries: count three digits from the right for ones, then groups of two for each higher Indian period.

To read a number, name each period left to right — for example 52,78,641 is fifty-two lakh, seventy-eight thousand, six hundred forty-one.

The International system groups in threes all the way (thousands, millions, billions). The same digit string can be commaed both ways; 1 crore equals 10 million.

Where the commas fall in each systemINDIAN — 3, then 2, then 24,56,78,901crore | lakh | thousand | onesINTERNATIONAL — 3 every time45,678,901millions | thousands | ones — always count from the RIGHT
Indian groups 3 then 2 then 2. International groups 3 every time.

Remember This

  • The digits never change between systems — only the grouping does.
  • Indian commas go 3, then 2, then 2 from the right: 4,56,78,901.
  • International commas go in 3s all the way: 45,678,901.
  • 1 million = 10 lakh, and 1 crore = 10 million.
  • Always count commas from the RIGHT, never from the left.
The two conversions worth memorising1 million = 10 lakh1 crore = 10 million
1 million = 10 lakh, and 1 crore = 10 million.

Try It Yourself

Write your school's total number of students, then the population of your city, then the population of India — all three in both systems, side by side.

Read each one aloud twice, once in each system. Notice that your mouth changes but the digits on the page do not.

Word Bank

Period
A group of digits separated by commas, like the thousands period.
Lakh
One hundred thousand, written 1,00,000 with five zeros.
Crore
One hundred lakh, written 1,00,00,000 with seven zeros.
Million
Ten lakh, written 1,000,000 with six zeros.
Place value
What a digit is worth because of where it sits in the number.

Questions

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