Maths carries 150 of the 300 marks — half the paper. And almost every maths question starts with reading a number correctly. Get this chapter right and the rest becomes easier.
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Natural numbers are the counting numbers: 1, 2, 3, 4, … They never end, and 0 is not a natural number. Add 0 and they become whole numbers.
🇮🇳 Indian System
| Period | Places |
|---|---|
| Ones | Ones, Tens, Hundreds |
| Thousands | Th, Ten Th |
| Lakhs | Lakh, Ten Lakh |
| Crores | Crore, Ten Crore |
Commas after 3, then every 2 digits:
3,45,678
Three lakh forty-five thousand six hundred seventy-eight
🌍 International System
| Period | Places |
|---|---|
| Ones | Ones, Tens, Hundreds |
| Thousands | Th, Ten Th, Hundred Th |
| Millions | Million, Ten M, Hundred M |
| Billions | Billion … |
Commas after every 3 digits:
345,678
Three hundred forty-five thousand six hundred seventy-eight
The two words examiners love to mix up:
Face value = the digit itself. Place value = digit × its place.
In 47852: the face value of 7 is 7, but its place value is 7 × 1000 = 7000.
🔍 Break up 5,84,209 (Indian system)
| Ten Lakh | Lakh | Ten Th | Th | Hundred | Ten | One |
|---|---|---|---|---|---|---|
| – | 5 | 8 | 4 | 2 | 0 | 9 |
| – | 5,00,000 | 80,000 | 4,000 | 200 | 0 | 9 |
Expanded form: 5,00,000 + 80,000 + 4,000 + 200 + 0 + 9
Try each one on rough paper first.
⚖️ How to compare two numbers
58,214 vs 58,092 → same digits; 5=5, 8=8, then 2 > 0, so 58,214 is bigger.
🎯 Rounding off
Look at the digit just to the right of the place you are rounding to:
4752 to the nearest hundred: the tens digit is 5 → round up → 4800.
🔁 Successor, predecessor & making numbers
Successor
the number just after → n + 1
successor of 4999 = 5000
Predecessor
the number just before → n − 1
predecessor of 7000 = 6999
Greatest / smallest
Greatest: big digits first.
Smallest: small digits first, but never start with 0.
Classic trap: using the digits 5, 0, 3, 7 — the smallest 4-digit number is 3057, not 0357. A number cannot begin with 0. The greatest is 7530.
These four properties turn slow sums into fast ones. Examiners test them directly, too.
Careful: subtraction and division are not commutative. 8 − 3 ≠ 3 − 8, and 8 ÷ 2 ≠ 2 ÷ 8. Only addition and multiplication can be reordered freely.
12 AISSEE-style questions. Remember: in the real paper each maths question is worth 3 marks, and there is no negative marking — so never leave one blank. 🍀
