Class 7 | Ganita Prakash Part-II | Chapter 4
🔢 Another Peek Beyond the Point
Decimal Multiplication · Division · Powers of 10
🔢 4.1 — Quick Recap of Decimals
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Decimals = Fractions with powers of 10!
3/10 = 0.3 4/100 = 0.04 67/1000 = 0.067
27.53 means:
2 Tens + 7 Ones + 5 Tenths + 3 Hundredths
= 20 + 7 + 0.5 + 0.03
3/10 = 0.3 4/100 = 0.04 67/1000 = 0.067
27.53 means:
2 Tens + 7 Ones + 5 Tenths + 3 Hundredths
= 20 + 7 + 0.5 + 0.03
🛒 Jonali's Spice Game!
50g = 50/1000 kg = 0.050 kg
100g = 100/1000 kg = 0.100 kg
250g = 250/1000 kg = 0.250 kg
Decimals make small measurements easy!
50g = 50/1000 kg = 0.050 kg
100g = 100/1000 kg = 0.100 kg
250g = 250/1000 kg = 0.250 kg
Decimals make small measurements easy!
Dividing by 10, 100, 1000... (move decimal LEFT):
123 ÷ 10 = 12.3 (decimal moves 1 place left)
123 ÷ 100 = 1.23 (decimal moves 2 places left)
123 ÷ 1000 = 0.123 (decimal moves 3 places left)
123 ÷ 10 = 12.3 (decimal moves 1 place left)
123 ÷ 100 = 1.23 (decimal moves 2 places left)
123 ÷ 1000 = 0.123 (decimal moves 3 places left)
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✖️ 4.2 — Decimal Multiplication
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How to Multiply Decimals:
Shortcut Rule:
Count total decimal places in both numbers → that's how many in the answer!
0.3 (1 place) × 0.4 (1 place) = 0.12 (2 places) ✅
Convert decimals to fractions: 0.3 × 0.4 = 3/10 × 4/10
Multiply the fractions: = 12/100
Convert back to decimal: = 0.12
Shortcut Rule:
Count total decimal places in both numbers → that's how many in the answer!
0.3 (1 place) × 0.4 (1 place) = 0.12 (2 places) ✅
More Examples:
9.5 × 5: Ignore decimals → 95 × 5 = 475 → 1 decimal place → 47.5
1.64 × 6: 164 × 6 = 984 → 2 decimal places → 9.84
5.7 × 13.3: 57 × 133 = 7581 → 2 decimal places → 75.81
9.5 × 5: Ignore decimals → 95 × 5 = 475 → 1 decimal place → 47.5
1.64 × 6: 164 × 6 = 984 → 2 decimal places → 9.84
5.7 × 13.3: 57 × 133 = 7581 → 2 decimal places → 75.81
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🔟 Multiplying by 10, 100, 1000
Move decimal point RIGHT when multiplying:
| Multiply by | Move decimal | Example |
|---|---|---|
| 10 | 1 place RIGHT → | 2.34 × 10 = 23.4 |
| 100 | 2 places RIGHT →→ | 2.34 × 100 = 234 |
| 1000 | 3 places RIGHT →→→ | 2.34 × 1000 = 2340 |
Divide = move LEFT, Multiply = move RIGHT!
÷10 → ← one place ×10 → → one place
÷100 → ← two places ×100 → → two places
Count zeros = count places!
÷10 → ← one place ×10 → → one place
÷100 → ← two places ×100 → → two places
Count zeros = count places!
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➗ 4.3 — Decimal Division
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Dividing a Decimal by Whole Number:
9.9 ÷ 3 = 3.3 (just divide, keep decimal in same position)
Dividing by a Decimal:
Convert divisor to whole number by multiplying both!
0.9 ÷ 0.3 = (0.9×10) ÷ (0.3×10) = 9 ÷ 3 = 3
7.5 ÷ 2.5 = 75 ÷ 25 = 3
9.9 ÷ 3 = 3.3 (just divide, keep decimal in same position)
Dividing by a Decimal:
Convert divisor to whole number by multiplying both!
0.9 ÷ 0.3 = (0.9×10) ÷ (0.3×10) = 9 ÷ 3 = 3
7.5 ÷ 2.5 = 75 ÷ 25 = 3
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Long Division with Decimals:
If dividing decimal by whole: divide normally, place decimal in quotient directly above dividend decimal
If dividing by decimal: multiply both by 10/100/1000 to make divisor a whole number
Then do normal long division
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📝 Quick Cheatsheet
× decimals:
Ignore decimal,
count places at end
Ignore decimal,
count places at end
×10 → move . right 1
×100 → right 2
×1000 → right 3
×100 → right 2
×1000 → right 3
÷10 → move . left 1
÷100 → left 2
÷1000 → left 3
÷100 → left 2
÷1000 → left 3
÷ decimal:
×both to remove ..
then divide!
×both to remove ..
then divide!
| Operation | Rule | Example |
|---|---|---|
| × two decimals | Multiply without dots, count total decimal places | 1.2 × 0.3 = 0.36 (2 places) |
| × by 10ⁿ | Shift decimal n places right | 4.56 × 100 = 456 |
| ÷ by 10ⁿ | Shift decimal n places left | 456 ÷ 100 = 4.56 |
| ÷ decimal | Multiply both by power of 10 first | 0.6 ÷ 0.2 = 6 ÷ 2 = 3 |
🌟 Chapter 4 Complete! 🌟
Made with ❤️ by @edugrown
Made with ❤️ by @edugrown