Large Numbers, Lakhs and Crores: Class 5 Study Guide
Big numbers appear in populations, distances and money. Place value lets us read them correctly.
In Class 5, children work with numbers beyond lakhs, up to crores. In the Indian system the places are ones, tens, hundreds, thousands, ten thousands, lakhs, ten lakhs, crores and ten crores. Commas go after the first three digits from the right and then after every two digits: 12,34,56,789.
In the international system, commas go after every three digits: 123,456,789. The same number is read as twelve crore thirty-four lakh fifty-six thousand seven hundred eighty-nine in the Indian system, and as one hundred twenty-three million four hundred fifty-six thousand seven hundred eighty-nine in the international system.
Place value chart
| Crores | Ten lakhs | Lakhs | Ten thousands | Thousands | Hundreds | Tens | Ones |
|---|---|---|---|---|---|---|---|
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
Comparing the two systems
1 lakh = 100,000 (a hundred thousand). 1 crore = 100 lakh = 10,000,000 (ten million). 10 lakh = 1 million. Being able to switch between the two is useful when reading news, maps and prices.
| Indian | Number | International |
|---|---|---|
| 1 lakh | 1,00,000 | one hundred thousand |
| 10 lakh | 10,00,000 | one million |
| 1 crore | 1,00,00,000 | ten million |
| 10 crore | 10,00,00,000 | one hundred million |
Comparing, ordering and rounding
Compare the number of digits first. The number with more digits is greater. If both have the same number of digits, compare from the left, place by place. To round to the nearest thousand, look at the hundreds digit: 5 or more rounds up. 46,380 rounds to 46,000, and 46,580 rounds to 47,000. Estimating helps check answers: 48,950 + 31,200 is about 49,000 + 31,000 = 80,000.
Thousands.
Hundreds.
Round up.
To keep the place value.
Worked examples and common mistakes
Example: Write 'three crore forty-two lakh five thousand' in figures: 3,42,05,000. Example: The population of a town is 4,56,789. Round to the nearest lakh: 5,00,000. Common mistakes: putting commas in the wrong places, leaving out zeros (writing 3,42,5000) and comparing digits without counting how many there are. Use a place value chart with zeros marked.
Check your understanding: model answers
1. 5,06,00,000. 2. 78,000. 3. 10,01,000, since it has 7 digits and the other has 6.
✨ Key Takeaways
- Indian system: 3 digits, then every 2 digits.
- 1 lakh = 1,00,000 and 1 crore = 1,00,00,000.
- More digits means a greater number.
- Rounding looks at the digit on the right.
💬 Questions for Discussion & Reflection
- Write 5 crore 6 lakh in figures.
- Round 78,462 to the nearest thousand.
- Which is greater: 9,87,654 or 10,01,000?