Decimal Fractions
Key Concepts
| # | Concept | Explanation |
|---|---|---|
| 1 | Decimal ↔ Fraction | Shift decimal right till number becomes integer → that many zeroes in denominator (0.37 → 37/100). |
| 2 | Like Decimals | Same number of digits after decimal (3.05, 12.60). Convert all to like form before +/–. |
| 3 | Unlike → Like | Annex zeroes on right; value unchanged (4.7 → 4.700). |
| 4 | Multiplication | a) ignore decimal → multiply integers; b) put decimal so total places = sum of places in factors (0.2×0.03=0.006). |
| 5 | Division | Shift both numbers till divisor becomes integer; then divide (3.5÷0.07 → 350÷7=50). |
| 6 | Recurring Decimal | Bar over repeating block; 0.333… = 0.3̄ = 1⁄3. |
| 7 | Comparison | Annex zeroes → compare left-to-right digit-wise. |
| 8 | Rounding | Look at next digit; ≥5 round up, else same; 3.476 → 3.48 (2 places). |
15 Practice MCQs
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0.0064 ÷ 0.04 = ? A 0.0016 B 0.016 C 0.16 D 1.6
Ans: C
Sol: 0.0064 ÷ 0.04 = 64 ÷ 400 = 0.16
Trick: Cancel 2 zeroes top & bottom → 64/400 = 16/100 = 0.16
Tag: Division of decimals -
Express 0.125 as a fraction in lowest terms. A 1/9 B 1/7 C 1/8 D 2/9
Ans: C
Sol: 0.125 = 125/1000 = 1/8
Trick: 125 is 1/8 of 1000
Tag: Decimal → Fraction -
Which is greatest: 0.7, 0.699, 0.7001, 0.701? A 0.7 B 0.699 C 0.7001 D 0.701
Ans: D
Sol: Annex → 0.7000, 0.6990, 0.7001, 0.7010 → 0.7010 largest
Tag: Comparison -
3.6 × 2.5 = ? A 9 B 8.9 C 9.1 D 90
Ans: A
Sol: 36×25=900; total 2 decimal places → 9.00 = 9
Trick: 2.5 = 10/4; 3.6×10/4 = 36/4 = 9
Tag: Decimal multiplication -
(0.3̄ + 0.2̄) equals A 0.5̄ B 0.6̄ C 0.54̄ D 0.4̄
Ans: A
Sol: 0.3̄ = 1/3, 0.2̄ = 2/9 → 1/3+2/9 = 5/9 = 0.5̄
Tag: Recurring decimals -
0.45 ÷ 1.5 × 0.2 = ? A 0.06 B 0.6 C 0.006 D 6
Ans: A
Sol: 0.45 ÷ 1.5 = 0.3; 0.3 × 0.2 = 0.06
Tag: Mixed operations -
Convert 7/8 to decimal. A 0.85 B 0.875 C 0.7825 D 0.8
Ans: B
Sol: 7×125 / 8×125 = 875/1000 = 0.875
Trick: 8×125=1000 → numerator also ×125
Tag: Fraction → Decimal -
12.345 rounded to 1 decimal place is A 12.4 B 12.3 C 12.35 D 12.34
Ans: B
Sol: 2nd decimal 4 <5 → 12.3
Tag: Rounding -
0.008 × 0.05 = ? A 0.004 B 0.0004 C 0.04 D 0.00004
Ans: B
Sol: 8×5=40; total 5 dec. places → 0.00040
Trick: Count zeroes: 3+2=5 → 4 preceded by 3 zeroes → 0.0004
Tag: Place-value multiplication -
If 1.08 ÷ x = 0.09 then x = ? A 12 B 1.2 C 0.12 D 120
Ans: A
Sol: x = 1.08 ÷ 0.09 = 108 ÷ 9 = 12
Tag: Decimal equation -
0.3 of 0.3 of 1000 = ? A 90 B 9 C 900 D 0.9
Ans: A
Sol: 0.3×0.3=0.09; 0.09×1000=90
Tag: ‘Of’ operator -
Which fraction is NOT equal to 0.04? A 1/25 B 4/100 C 2/50 D 1/20
Ans: D
Sol: 1/20 = 0.05 ≠ 0.04
Tag: Equivalent decimals -
0.6̄ ÷ 0.3̄ = ? A 2 B 0.2 C 0.5 D 1
Ans: A
Sol: 0.6̄ = 2/3, 0.3̄ = 1/3 → (2/3)/(1/3)=2
Tag: Recurring division -
5.5 – 2.55 + 1.005 = ? A 3.955 B 4.055 C 3.995 D 4.105
Ans: A
Sol: 5.500 – 2.550 = 2.950; +1.005 = 3.955
Tag: Addition/subtraction -
A rod 6.75 m is cut into 0.25 m pieces. Number of pieces is A 25 B 26 C 27 D 28
Ans: C
Sol: 6.75 ÷ 0.25 = 675 ÷ 25 = 27
Trick: 0.25 = 1/4; 6.75×4 = 27
Tag: Real-life division
Speed Tricks
| Situation | Shortcut | Example |
|---|---|---|
| ÷ 0.25 | × 4 | 3.25 ÷ 0.25 = 3.25×4 = 13 |
| ÷ 0.5 | × 2 | 7.8 ÷ 0.5 = 15.6 |
| ÷ 0.2 | × 5 | 4.3 ÷ 0.2 = 21.5 |
| × 0.25 | ÷ 4 | 9.6×0.25 = 9.6÷4 = 2.4 |
| Compare quickly | Annex zeroes to same length, compare digit-wise | 0.807 ? 0.81 → 0.807 vs 0.810 → 0.810 wins |
Quick Revision
| Point | Detail |
|---|---|
| 1 | Annexing zeroes right of decimal does not change value. |
| 2 | Move decimal right in both numbers while dividing → divisor becomes integer. |
| 3 | 0.1̄ = 1/9; 0.01̄ = 1/90; 0.abc̄ = (abc–ab)/900. |
| 4 | Shortcut 0.2 = 1/5, 0.25 = 1/4, 0.5 = 1/2, 0.125 = 1/8. |
| 5 | Product has total decimal places = sum in factors. |
| 6 | While +/–, vertically align decimal points, fill zeroes. |
| 7 | To round, look one extra digit; 5 or above → round up. |
| 8 | ‘Of’ means multiply; 0.2 of 0.3 of x = 0.06x. |
| 9 | 0.6̄ + 0.3̄ = 1.0 exactly; 0.9̄ = 1. |
| 10 | In exam, convert all to integers by powers of 10 → faster mental steps. |
BETA
