Large Numbers Around Us · Lesson 3 of 9
Crores, Millions, and Billions
“Translate between Indian and International names without changing the number.”
• Explain the relationships among lakh, crore, million, billion, and arab. • Group and read long numerals in both naming systems. • Write numerals from number names while preserving zero groups. • Compare quantities after converting them to a common unit.
Two languages for the same quantity
A number can have two different names without changing its value. Indian grouping uses thousands, lakhs, and crores, while International grouping uses thousands, millions, and billions. The digits keep the same decimal place values; only the grouping and the names change.
Ten lakhs make one million, because 10 × 1,00,000 = 10,00,000 = 1,000,000. One hundred lakhs make one crore, equal to ten million. Continuing upward, one hundred crores make one billion, also called one arab in the extended Indian naming system.
| Quantity | Indian grouping and name | International grouping and name |
|---|---|---|
| One thousand | 1,000 — one thousand | 1,000 — one thousand |
| Ten thousand | 10,000 — ten thousand | 10,000 — ten thousand |
| One lakh | 1,00,000 — one lakh | 100,000 — one hundred thousand |
| Ten lakh | 10,00,000 — ten lakh | 1,000,000 — one million |
| One crore | 1,00,00,000 — one crore | 10,000,000 — ten million |
| Ten crore | 10,00,00,000 — ten crore | 100,000,000 — one hundred million |
| One hundred crore | 1,00,00,00,000 — one arab | 1,000,000,000 — one billion |
One million is 1 followed by six zeros. One billion is one thousand million, or 1 followed by nine zeros, in the International system used here.
The source notes that lakh-and-crore naming is also used in several neighbouring countries, including Nepal, Bangladesh, and Sri Lanka. The Indian terms lakh and crore are related to older words laksha and koti. Naming conventions are useful when reading information from different places. Here “International” always means the system in which a billion is one thousand million.
Problem
Express one billion as a number of lakhs.
- 1.One billion is 1,000,000,000 and one lakh is 100,000.
- 2.1,000,000,000 ÷ 100,000 = 10,000.
- 3.Therefore 10,000 lakhs make a billion. Equivalently, 100 crores × 100 lakhs per crore = 10,000 lakhs.
| Name | Number of zeros after 1 |
|---|---|
| Lakh | 5 |
| Crore | 7 |
| Million | 6 |
| Billion or arab | 9 |
| Thousand lakh | 8: 1,000 × 1,00,000 = 10,00,00,000 |
Commas show the grouping
Write commas from the right because the ones, tens, and hundreds form the final group in both systems. In Indian notation, place the first comma after three digits and the remaining commas after pairs. In International notation, continue using groups of three throughout.
Problem
Group and read 9876501234 in both systems.
- 1.Indian grouping gives 9,87,65,01,234. Reading by groups gives nine arab eighty-seven crore sixty-five lakh one thousand two hundred thirty-four.
- 2.Without using arab, the same number is nine hundred eighty-seven crore sixty-five lakh one thousand two hundred thirty-four.
- 3.International grouping gives 9,876,501,234: nine billion eight hundred seventy-six million five hundred one thousand two hundred thirty-four.
- 4.Remove all commas from either form and the original digit string is identical.
| International grouping | Indian grouping | Indian name | International name |
|---|---|---|---|
| 4,050,678 | 40,50,678 | Forty lakh fifty thousand six hundred seventy-eight | Four million fifty thousand six hundred seventy-eight |
| 48,121,620 | 4,81,21,620 | Four crore eighty-one lakh twenty-one thousand six hundred twenty | Forty-eight million one hundred twenty-one thousand six hundred twenty |
| 20,022,002 | 2,00,22,002 | Two crore twenty-two thousand two | Twenty million twenty-two thousand two |
| 246,813,579 | 24,68,13,579 | Twenty-four crore sixty-eight lakh thirteen thousand five hundred seventy-nine | Two hundred forty-six million eight hundred thirteen thousand five hundred seventy-nine |
| 345,000,543 | 34,50,00,543 | Thirty-four crore fifty lakh five hundred forty-three | Three hundred forty-five million five hundred forty-three |
| 1,020,304,050 | 1,02,03,04,050 | One arab two crore three lakh four thousand fifty | One billion twenty million three hundred four thousand fifty |
A group such as 000 means that no quantity of that group is present. In 345,000,543 there are 345 million, no thousands, and 543 ones. Omitting the word “thousand” when reading is correct; omitting the three zeros when writing would change the number.
Writing names back into digits
Build the number by adding the quantities named in the sentence. A place-value chart helps you reserve room for every group, including groups that are not mentioned. Do not join the spoken numbers as unpadded digit strings.
Problem
Write one crore one lakh one thousand ten, and one billion one million one thousand one.
- 1.The first name gives 1,00,00,000 + 1,00,000 + 1,000 + 10 = 1,01,01,010.
- 2.Its groups are 1 crore | 01 lakh | 01 thousand | 010. The final group needs three digits.
- 3.The second gives 1,000,000,000 + 1,000,000 + 1,000 + 1 = 1,001,001,001.
- 4.Its groups are 1 billion | 001 million | 001 thousand | 001. Every group after the first needs three digits. In Indian grouping the same digits are 1,00,10,01,001.
| Number name | Numeral |
|---|---|
| Ten crore twenty lakh thirty thousand forty | 10,20,30,040 |
| Nine billion eighty million seven hundred thousand six hundred | 9,08,07,00,600 (International: 9,080,700,600) |
Compare using one common unit
Comparing only the number of spoken words can be misleading: 500 lakh sounds smaller than 5 million if we ignore the units, yet it is larger. Convert both quantities into lakhs, millions, crores, or ordinary digits before comparing. Equal units make the comparison direct.
Problem
Compare the pairs after converting their units.
- 1.30 thousand = 30,000 and 3 lakh = 3,00,000, so 30 thousand < 3 lakh.
- 2.500 lakh = 50 million, so 500 lakh > 5 million.
- 3.800 thousand = 0.8 million, so 800 thousand < 8 million.
- 4.60 billion = 6,000 crore, so 640 crore < 60 billion.
10,00,000 and 1,000,000 represent the same number. A misplaced or omitted digit changes the value; correctly regrouping the same digits changes only how the number is read. One crore is ten million, not one million.
Quiz
One crore equals:
How many lakhs make one billion?
Which is the International grouping of 123456789?
One billion one million one thousand one is:
Which comparison is correct?
How many zeros follow 1 in one arab?
Practice Problems
- Write 4050678, 48121620, and 20022002 with commas and names in both systems.
- Write 246813579, 345000543, and 1020304050 in both systems. Explain how empty groups are represented.
- Convert 8 million into lakhs and 35 crore into millions.
- Write “one crore one lakh one thousand ten”, “ten crore twenty lakh thirty thousand forty”, and “nine billion eighty million seven hundred thousand six hundred” as numerals.
- Compare 250 lakh with 20 million, and 75 crore with 1 billion, using a common unit.
- Find the number of zeros in one thousand lakh and explain the result using multiplication.
- Explain why removing commas from two correct groupings must leave exactly the same digit string.
Key Takeaways
• Indian commas follow the 3-2-2 pattern from the right; International commas follow 3-3-3. • One million is ten lakh, and one crore is ten million. • One billion is one arab, one hundred crore, or ten thousand lakh. • Number names change with the naming system, while the value stays the same. • Empty groups require zero placeholders in written numerals. • Convert quantities to a common unit before comparing them.