🔄 Fraction-Percentage-Decimal Conversions
The complete conversion table that lets you replace ugly percentages with clean fractions instantly — memorise this and save 10+ seconds per question
Fraction-Percentage-Decimal Conversions
Here is the single most powerful weapon for simplification and approximation questions. When you see 33.33% of 270 in an exam, you should NOT multiply 0.3333 × 270. You should instantly think (1/3) × 270 = 90. That replacement saves 10–15 seconds — and across 5–10 questions, it decides whether you clear the cutoff.
This lesson gives you the complete conversion table, the patterns behind it, and the memory tricks to lock it in permanently.
The Core Table — Fractions 1/2 Through 1/18
This is the non-negotiable foundation. Every competitive exam aspirant must have these at instant recall.
| Fraction | Decimal | Percentage |
|---|---|---|
| 1/2 | 0.5 | 50% |
| 1/3 | 0.333... | 33.33% |
| 1/4 | 0.25 | 25% |
| 1/5 | 0.2 | 20% |
| 1/6 | 0.1666... | 16.67% |
| 1/7 | 0.142857... | 14.28% |
| 1/8 | 0.125 | 12.5% |
| 1/9 | 0.111... | 11.11% |
| 1/10 | 0.1 | 10% |
| 1/11 | 0.0909... | 9.09% |
| 1/12 | 0.0833... | 8.33% |
| 1/13 | 0.0769... | 7.69% |
| 1/14 | 0.0714... | 7.14% |
| 1/15 | 0.0666... | 6.67% |
| 1/16 | 0.0625 | 6.25% |
| 1/17 | 0.0588... | 5.88% |
| 1/18 | 0.0555... | 5.56% |
How to read this table: When a question says "find 14.28% of 350", your brain should fire: 14.28% = 1/7, so the answer is 350/7 = 50. No calculator. No long multiplication. Just division.
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Fraction-Percentage-Decimal Conversions
Here is the single most powerful weapon for simplification and approximation questions. When you see 33.33% of 270 in an exam, you should NOT multiply 0.3333 × 270. You should instantly think (1/3) × 270 = 90. That replacement saves 10–15 seconds — and across 5–10 questions, it decides whether you clear the cutoff.
This lesson gives you the complete conversion table, the patterns behind it, and the memory tricks to lock it in permanently.
The Core Table — Fractions 1/2 Through 1/18
This is the non-negotiable foundation. Every competitive exam aspirant must have these at instant recall.
| Fraction | Decimal | Percentage |
|---|---|---|
| 1/2 | 0.5 | 50% |
| 1/3 | 0.333... | 33.33% |
| 1/4 | 0.25 | 25% |
| 1/5 | 0.2 | 20% |
| 1/6 | 0.1666... | 16.67% |
| 1/7 | 0.142857... | 14.28% |
| 1/8 | 0.125 | 12.5% |
| 1/9 | 0.111... | 11.11% |
| 1/10 | 0.1 | 10% |
| 1/11 | 0.0909... | 9.09% |
| 1/12 | 0.0833... | 8.33% |
| 1/13 | 0.0769... | 7.69% |
| 1/14 | 0.0714... | 7.14% |
| 1/15 | 0.0666... | 6.67% |
| 1/16 | 0.0625 | 6.25% |
| 1/17 | 0.0588... | 5.88% |
| 1/18 | 0.0555... | 5.56% |
How to read this table: When a question says "find 14.28% of 350", your brain should fire: 14.28% = 1/7, so the answer is 350/7 = 50. No calculator. No long multiplication. Just division.
The 1/8 Family — Your Secret Weapon
The eighths appear extremely frequently in banking exams because 12.5%, 37.5%, 62.5%, and 87.5% look intimidating but become trivial with fractions.
| Percentage | Fraction | Pattern |
|---|---|---|
| 12.5% | 1/8 | 1 × 12.5 |
| 25% | 2/8 = 1/4 | 2 × 12.5 |
| 37.5% | 3/8 | 3 × 12.5 |
| 50% | 4/8 = 1/2 | 4 × 12.5 |
| 62.5% | 5/8 | 5 × 12.5 |
| 75% | 6/8 = 3/4 | 6 × 12.5 |
| 87.5% | 7/8 | 7 × 12.5 |
The pattern: Each step adds 12.5%. So the eighths family is just multiples of 12.5%.
Speed application: 37.5% of 480 = (3/8) × 480 = 3 × 60 = 180. Try doing 0.375 × 480 by hand — it takes 4x longer.
The 1/7 Family — The Cyclic Magic Number
The sevenths are special because they all cycle through the same six digits: 142857.
| Fraction | Decimal | Percentage |
|---|---|---|
| 1/7 | 0.142857142857... | 14.28% |
| 2/7 | 0.285714285714... | 28.57% |
| 3/7 | 0.428571428571... | 42.86% |
| 4/7 | 0.571428571428... | 57.14% |
| 5/7 | 0.714285714285... | 71.43% |
| 6/7 | 0.857142857142... | 85.71% |
The magic: Every fraction of 7 uses the same six digits (1, 4, 2, 8, 5, 7) — just starting from a different position in the cycle. Memorise 142857 once and you know all six fractions.
Memory trick: 142857 × 7 = 999999. This is why the cycle works — it's the repeating block of 1/7 in base 10.
The 1/9 Family — Repeating Single Digits
The ninths are the easiest family to memorise because each one is just a repeating single digit.
| Fraction | Decimal | Percentage |
|---|---|---|
| 1/9 | 0.111... | 11.11% |
| 2/9 | 0.222... | 22.22% |
| 3/9 = 1/3 | 0.333... | 33.33% |
| 4/9 | 0.444... | 44.44% |
| 5/9 | 0.555... | 55.56% |
| 6/9 = 2/3 | 0.666... | 66.67% |
| 7/9 | 0.777... | 77.78% |
| 8/9 | 0.888... | 88.89% |
The pattern: x/9 = 0.xxx... The numerator just repeats. So 4/9 = 0.4444..., 7/9 = 0.7777..., and so on.
Why this matters: When you see 44.44%, you should instantly think 4/9. When you see 77.78%, think 7/9.
The 1/11 Family — Repeating Two-Digit Patterns
The elevenths follow a beautiful pattern: each is a repeating two-digit block.
| Fraction | Decimal | Percentage |
|---|---|---|
| 1/11 | 0.0909... | 9.09% |
| 2/11 | 0.1818... | 18.18% |
| 3/11 | 0.2727... | 27.27% |
| 4/11 | 0.3636... | 36.36% |
| 5/11 | 0.4545... | 45.45% |
| 6/11 | 0.5454... | 54.54% |
| 7/11 | 0.6363... | 63.64% |
| 8/11 | 0.7272... | 72.73% |
| 9/11 | 0.8181... | 81.82% |
| 10/11 | 0.9090... | 90.91% |
The pattern: x/11 = 0.(09 × x)(09 × x)... The repeating block is always 9 times the numerator. So 3/11 → 09 × 3 = 27 → 0.2727... And 7/11 → 09 × 7 = 63 → 0.6363...
Extended Fractions — The Rest of the Arsenal
These come up less frequently but still appear in exams. Know them well enough to recognise them.
Twelfths:
| Fraction | Decimal | Percentage |
|---|---|---|
| 1/12 | 0.0833... | 8.33% |
| 5/12 | 0.4166... | 41.67% |
| 7/12 | 0.5833... | 58.33% |
| 11/12 | 0.9166... | 91.67% |
Fifths and their multiples:
| Fraction | Decimal | Percentage |
|---|---|---|
| 1/5 | 0.2 | 20% |
| 2/5 | 0.4 | 40% |
| 3/5 | 0.6 | 60% |
| 4/5 | 0.8 | 80% |
Sixths:
| Fraction | Decimal | Percentage |
|---|---|---|
| 1/6 | 0.1666... | 16.67% |
| 5/6 | 0.8333... | 83.33% |
Percentages Above 100%
These appear in profit & loss, data interpretation, and mixture problems. The fraction form makes calculation trivial.
| Percentage | Fraction | Use case |
|---|---|---|
| 125% | 5/4 | 25% profit → selling price = 5/4 of cost |
| 133.33% | 4/3 | 33.33% profit → SP = 4/3 of CP |
| 150% | 3/2 | 50% increase |
| 166.67% | 5/3 | 66.67% increase |
| 175% | 7/4 | 75% increase |
| 200% | 2 | Doubling |
| 250% | 5/2 | 150% increase |
| 300% | 3 | Tripling |
| 350% | 7/2 | 250% increase |
| 400% | 4 | Quadrupling |
Key insight: When a question says "A is 125% of B", that means A = (5/4) × B. When it says "A is 25% more than B", it also means A = (5/4) × B. Same fraction, different wording.
How to Use in Exams — Worked Examples
The technique is always the same: spot the percentage, replace with fraction, simplify.
Example 1: Direct percentage
Find 37.5% of 640.
37.5% = 3/8
(3/8) × 640 = 3 × 80 = 240
Time taken: 3 seconds.
Example 2: Approximation
14.28% of 2107 + 33.33% of 897 = ?
14.28% ≈ 1/7, so 1/7 × 2107 ≈ 2100/7 = 300 (approx 301)
33.33% = 1/3, so 1/3 × 897 ≈ 900/3 = 300 (approx 299)
Answer ≈ 300 + 299 = 599 (actual: 600.97)
Time taken: 5 seconds. Without fractions, this takes 30+ seconds.
Example 3: Percentage change
A shopkeeper buys at Rs 480 and sells at 62.5% profit. Find selling price.
62.5% profit → SP = (100% + 62.5%) of CP = 162.5% of CP
But think in fractions: 62.5% = 5/8, so SP = (1 + 5/8) × 480 = (13/8) × 480 = 13 × 60 = 780
Time taken: 5 seconds.
Example 4: Reverse percentage
88.89% of a number is 3200. Find the number.
88.89% = 8/9
So (8/9) × x = 3200
x = 3200 × (9/8) = 400 × 9 = 3600
Time taken: 4 seconds.
Memory Tricks — How to Lock This In
You do NOT memorise this table by staring at it. You memorise it by understanding the patterns.
Pattern 1: The 1/9 family is repeating digits. 1/9 = 0.111..., 2/9 = 0.222..., etc. Numerator repeats. Done.
Pattern 2: The 1/11 family is 09 × numerator. 3/11 → 09 × 3 = 27 → 0.2727... Multiply 9 by the numerator to get the repeating block.
Pattern 3: The 1/7 family cycles through 142857. Start with 142857. For 2/7, start from the "2" position: 285714. For 3/7, start from "4": 428571. The cycle never breaks.
Pattern 4: The 1/8 family is multiples of 12.5. Just count: 12.5, 25, 37.5, 50, 62.5, 75, 87.5. Seven steps from 1/8 to 7/8.
Pattern 5: Complementary pairs add to 100%. 1/7 + 6/7 = 100%. So if you know 1/7 = 14.28%, then 6/7 = 85.72%. This halves the memorisation work for every family.
Pattern 6: The "near" percentages.
- 14.28% ≈ 14.3% → think 1/7
- 16.67% ≈ 16.7% → think 1/6
- 8.33% ≈ 8.3% → think 1/12
- 6.25% → think 1/16
Daily practice routine: Pick 5 random percentages from this lesson. Convert to fractions in your head. Then pick 5 random numbers and find those percentages using fractions. Do this for 10 minutes a day for one week — after that, the conversions become automatic.
Mixed-Number Percentages — The "x and Fraction" Forms
These percentages look intimidating at first glance, but they are just familiar fractions written in disguise. When you see 14 2/7% in a question, your brain should fire: that's 1/7.
The Sevenths Family:
| Percentage | As Mixed Number | Fraction |
|---|---|---|
| 14 2/7% | 14 + 2/7 | 1/7 |
| 28 4/7% | 28 + 4/7 | 2/7 |
| 42 6/7% | 42 + 6/7 | 3/7 |
| 57 1/7% | 57 + 1/7 | 4/7 |
| 71 3/7% | 71 + 3/7 | 5/7 |
| 85 5/7% | 85 + 5/7 | 6/7 |
Why this works: 1/7 = 0.142857... = 14.2857...%. The "14" becomes the whole part, and 2/7 is the fractional part (since 0.2857... = 2/7). Each subsequent seventh just multiplies: 2/7 = 28.5714...% = 28 4/7%, and so on.
The Twelfths Family:
| Percentage | As Mixed Number | Fraction |
|---|---|---|
| 8 1/3% | 8 + 1/3 | 1/12 |
| 41 2/3% | 41 + 2/3 | 5/12 |
| 58 1/3% | 58 + 1/3 | 7/12 |
| 91 2/3% | 91 + 2/3 | 11/12 |
Why this works: 1/12 = 0.08333... = 8.333...% = 8 1/3%. The other twelfths follow the same logic. Note that 2/12 = 1/6, 3/12 = 1/4, etc. — those simplify to families you already know. Only the odd twelfths (1, 5, 7, 11) produce these mixed-number forms.
Worked example:
Find 71 3/7% of 1120 + 28 4/7% of 980
71 3/7% = 5/7, and 28 4/7% = 2/7
(5/7) × 1120 = 5 × 160 = 800
(2/7) × 980 = 2 × 140 = 280
Answer: 800 + 280 = 1080
Without the conversion, you would be multiplying 71.4285... × 1120 by hand. With fractions: 5 seconds.
How to recognise them in exams: Look for percentages with fraction remainders — especially thirds and sevenths. If you see any percentage with "/7" or "/3" in the fractional part, immediately check if it belongs to the sevenths or twelfths family. These appear frequently in IBPS, SBI, and RRB quantitative aptitude sections.
Quick verification trick: Multiply your fraction by 100 to confirm. For example: 5/12 × 100 = 500/12 = 41 8/12 = 41 2/3. It checks out.
Quick Reference — The 20 Most Tested Conversions
If you're short on time, memorise these first. They cover 90%+ of exam questions:
| # | Percentage | Fraction |
|---|---|---|
| 1 | 10% | 1/10 |
| 2 | 12.5% | 1/8 |
| 3 | 14.28% | 1/7 |
| 4 | 16.67% | 1/6 |
| 5 | 20% | 1/5 |
| 6 | 25% | 1/4 |
| 7 | 33.33% | 1/3 |
| 8 | 37.5% | 3/8 |
| 9 | 40% | 2/5 |
| 10 | 50% | 1/2 |
| 11 | 62.5% | 5/8 |
| 12 | 66.67% | 2/3 |
| 13 | 75% | 3/4 |
| 14 | 80% | 4/5 |
| 15 | 87.5% | 7/8 |
| 16 | 11.11% | 1/9 |
| 17 | 9.09% | 1/11 |
| 18 | 125% | 5/4 |
| 19 | 133.33% | 4/3 |
| 20 | 150% | 3/2 |
Master this table. It is the single highest-ROI investment of study time for any quantitative aptitude exam.