Place value: every place is 10 times bigger
Our numbers use only ten digits, 0 to 9. The place of a digit tells its value. Moving one place to the left makes the value 10 times bigger.
In 4,07,325 the 4 is in the lakhs place, so it is worth 4,00,000. The 0 just keeps the ten-thousands place empty.
| Place | Value |
|---|---|
| Ones | 1 |
| Tens | 10 |
| Hundreds | 100 |
| Thousands | 1,000 |
| Ten thousands | 10,000 |
| Lakhs | 1,00,000 |
| Ten lakhs | 10,00,000 |
| Crores | 1,00,00,000 |
| Ten crores | 10,00,00,000 |
Commas and number names in the Indian system
Rule: start from the right. Put the first comma after 3 digits. Then put a comma after every 2 digits.
Example: 765432109 → 76,54,32,109. Read each group with its name: seventy-six crore fifty-four lakh thirty-two thousand one hundred nine.
- Group names from the right: ones (3 digits), thousands, lakhs, crores.
- Above crores some people say arab (100 crore) and kharab (100 arab), but in everyday use we say "100 crore", "1,000 crore" and so on.
- Never put "s" on lakh or crore when reading: "five lakh", not "five lakhs".
Indian vs international system
The international system groups digits in 3s: ones, thousands, millions, billions.
| Indian | International |
|---|---|
| 1 lakh = 1,00,000 | 100 thousand = 100,000 |
| 10 lakh = 10,00,000 | 1 million = 1,000,000 |
| 1 crore = 1,00,00,000 | 10 million = 10,000,000 |
| 100 crore = 1,00,00,00,000 | 1 billion = 1,000,000,000 |
To convert: remove all commas, then put the new commas. Or use the links: lakh ÷ 10 = million; crore × 10 = million.
Traditional Indian ways of writing numbers
Indian thinkers wrote about very large numbers more than 2,500 years ago. Each ×10 step had a name: eka (1), dasha (10), shata (100), sahasra (1,000), ayuta (10,000), laksha (1,00,000), prayuta (10,00,000), koti (1,00,00,000). Our words lakh and crore come from laksha and koti.
Three big ideas came from India:
- Place value with only ten symbols.
- Zero (shunya) as a real number and as an empty place.
- Old number scripts such as Brahmi grew into the digits 0–9 the whole world uses today (often called Hindu–Arabic numerals).
Poets sometimes hid numbers in words (for example "eyes" for 2, "moon" for 1), and the Katapayadi system matched letters to digits so long numbers could be remembered as verses.
Try it at home
Find three big numbers in a newspaper (population, prices, cricket earnings). Write each in Indian commas and international commas, then read them aloud both ways. Check with the sliders in the 3D.
Key formulas and definitions
- 1 lakh = 1,00,000 = 10⁵ = 100 thousand
- 10 lakh = 1 million = 10⁶
- 1 crore = 100 lakh = 10⁷ = 10 million
- 100 crore = 1 billion = 10⁹
- Indian commas: 3, then 2, 2, 2 … from the right
- International commas: 3, 3, 3 … from the right
Worked examples
1. Put Indian commas in 5207804 and write its name.
From the right: 804 | 07 | 52 → 52,07,804. Name: fifty-two lakh seven thousand eight hundred four.
2. How many zeros are there in 1 crore?
1 crore = 1,00,00,000. Count the zeros: 7.
3. Write 3 crore 40 lakh 6 thousand 25 in figures.
Crores: 3 | lakhs: 40 | thousands: 06 | ones: 025 → 3,40,06,025.
4. Change 45,60,000 into the international system.
Remove commas: 4560000. Groups of 3 from the right: 4,560,000. That is 4 million 560 thousand (4.56 million).
5. A city has 2.3 million people. How many lakh is that?
1 million = 10 lakh, so 2.3 million = 23 lakh = 23,00,000.
6. A film earned ₹ 250 crore. Write this in billions of rupees.
100 crore = 1 billion, so 250 crore = 2.5 billion rupees.
Common mistakes
- Putting commas after every 3 digits when the question asks for the Indian system.
- Counting the lakh as 4 zeros. 1 lakh has 5 zeros.
- Thinking 1 million = 1 crore. 1 million is only 10 lakh.
- Forgetting zeros for empty places, e.g. writing 3 crore 5 lakh as 3,5,00,000 instead of 3,05,00,000.