Comparing Numbers
Rule 1 — Number of Digits
The number with more digits is always greater.
| Number A | Number B | Greater |
|---|---|---|
| 999 | 1000 | 1000 (4 digits > 3 digits) |
| 9999 | 10000 | 10000 |
Rule 2 — Same Number of Digits
Compare left to right, digit by digit. First differing digit decides.
Example: Compare 4567 and 4589
- Thousands: 4 = 4
- Hundreds: 5 = 5
- Tens: 6 < 8 → so 4589 > 4567
Place Value — Indian Number System
| Period | Place | Value |
|---|---|---|
| Crores | Crores | 1,00,00,000 |
| Crores | Ten Crores | 10,00,00,000 |
| Lakhs | Lakhs | 1,00,000 |
| Lakhs | Ten Lakhs | 10,00,000 |
| Thousands | Thousands | 1,000 |
| Thousands | Ten Thousands | 10,000 |
| Ones | Hundreds | 100 |
| Ones | Tens | 10 |
| Ones | Ones | 1 |
Commas in Indian system: after every 2 digits from the right (except first group of 3). Example: 4,75,320 reads as "four lakh seventy-five thousand three hundred twenty"
Place Value — International Number System
| Period | Place | Value |
|---|---|---|
| Millions | Millions | 1,000,000 |
| Millions | Ten Millions | 10,000,000 |
| Thousands | Thousands | 1,000 |
| Thousands | Ten Thousands | 10,000 |
| Thousands | Hundred Thousands | 1,00,000 |
| Ones | Hundreds | 100 |
| Ones | Tens | 10 |
| Ones | Ones | 1 |
Commas in International system: after every 3 digits from the right. Example: 4,753,200 reads as "four million seven hundred fifty-three thousand two hundred"
Quick Conversion
- 1 lakh = 1,00,000 = 100 thousand
- 10 lakh = 10,00,000 = 1 million
- 1 crore = 1,00,00,000 = 10 million
Large Numbers in Practice
| In Figures | Indian System | International System |
|---|---|---|
| 5,00,000 | 5 lakh | 500 thousand |
| 10,00,000 | 10 lakh | 1 million |
| 1,00,00,000 | 1 crore | 10 million |
Estimation
Rounding rules:
- If the digit to be dropped is < 5, round down (keep the digit same).
- If the digit to be dropped is ≥ 5, round up (increase the digit by 1).
Rounding to Nearest 10
- 47 → 50 (7 ≥ 5, round up)
- 43 → 40 (3 < 5, round down)
Rounding to Nearest 100
- 473 → 500 (7 ≥ 5, round up)
- 423 → 400 (2 < 5, round down)
Estimating Sum/Difference
Round each number, then add/subtract. Example: 5678 + 2345 ≈ 5700 + 2300 = 8000
Roman Numerals
| Symbol | Value |
|---|---|
| I | 1 |
| V | 5 |
| X | 10 |
| L | 50 |
| C | 100 |
| D | 500 |
| M | 1000 |
Rules
1. Repeat a symbol up to 3 times: III = 3, XXX = 30. 2. Smaller before larger = subtract: IV = 4, IX = 9, XL = 40, XC = 90, CD = 400, CM = 900. 3. Smaller after larger = add: VI = 6, XV = 15, LX = 60. 4. V, L, D are never repeated or subtracted.
Examples
- 14 = XIV (10 + 4 = X + IV)
- 39 = XXXIX (30 + 9)
- 44 = XLIV (40 + 4)
- 75 = LXXV (50 + 25)
- 90 = XC
- 99 = XCIX
Key Vocabulary
| Term | Meaning |
|---|---|
| Place value | Value of a digit based on its position |
| Face value | The digit itself, regardless of position |
| Estimation | Finding an approximate value |
| Rounding | Replacing a number with a close, simpler number |
| Roman numeral | Number system using letters (I, V, X, L, C, D, M) |
Exam Tips
- Indian vs International number system — know the periods and comma placement for both; draw the place value table in answers.
- 1 crore = 10 million and 10 lakh = 1 million — direct 1-mark conversion questions.
- For estimation, always state to the nearest 10/100/1000 as asked.
- Roman numerals up to 100 are standard — IV, IX, XL, XC are the subtractive forms.
- Face value of 7 in 4738 = 7. Place value of 7 in 4738 = 700 — both are asked.