Fraction to Decimal to Percentage Matrix (1/1 to 1/20)
This matrix converts the unit fractions 1/1 to 1/20 into decimals and percentages, showing which decimals terminate and which repeat. Use the live converter for any fraction, decimal or percentage.
1/20.5 = 50%Half
1/30.333... = 33.33%Repeating decimal
1/40.25 = 25%Quarter
1/80.125 = 12.5%Eighth
Fraction to Decimalnumerator ÷ denominatorExample: 3/8 = 3 ÷ 8 = 0.375
Decimal to Percentdecimal × 100Example: 0.375 × 100 = 37.5%
Fraction, Decimal & Percentage Converter
Tip: open this page with ?frac=1/8 (any fraction, such as 3/4) to start with it and highlight its row. In results, a repeating block is shown in brackets: 0.(3) means 0.333... forever. For a repeating decimal such as 0.3333, use the fraction tab with 1/3.
| Fraction | Decimal Form | Percentage (%) | Precision String | Copy Row |
|---|---|---|---|---|
| 1/1 | 1 | 100% | Exact; whole number | |
| 1/2 | 0.5 | 50% | Exact; 1 decimal place | |
| 1/3 | 0.3 | 33.3% | Repeating (period 1): 0.3333 to 4 d.p., 33.33% to 2 d.p. | |
| 1/4 | 0.25 | 25% | Exact; 2 decimal places | |
| 1/5 | 0.2 | 20% | Exact; 1 decimal place | |
| 1/6 | 0.16 | 16.6% | Repeating (period 1): 0.1667 to 4 d.p., 16.67% to 2 d.p. | |
| 1/7 | 0.142857 | 14.285714% | Repeating (period 6): 0.1429 to 4 d.p., 14.29% to 2 d.p. | |
| 1/8 | 0.125 | 12.5% | Exact; 3 decimal places | |
| 1/9 | 0.1 | 11.1% | Repeating (period 1): 0.1111 to 4 d.p., 11.11% to 2 d.p. | |
| 1/10 | 0.1 | 10% | Exact; 1 decimal place | |
| 1/11 | 0.09 | 9.09% | Repeating (period 2): 0.0909 to 4 d.p., 9.09% to 2 d.p. | |
| 1/12 | 0.083 | 8.3% | Repeating (period 1): 0.0833 to 4 d.p., 8.33% to 2 d.p. | |
| 1/13 | 0.076923 | 7.692307% | Repeating (period 6): 0.0769 to 4 d.p., 7.69% to 2 d.p. | |
| 1/14 | 0.0714285 | 7.142857% | Repeating (period 6): 0.0714 to 4 d.p., 7.14% to 2 d.p. | |
| 1/15 | 0.06 | 6.6% | Repeating (period 1): 0.0667 to 4 d.p., 6.67% to 2 d.p. | |
| 1/16 | 0.0625 | 6.25% | Exact; 4 decimal places | |
| 1/17 | 0.0588235294117647 | 5.8823529411764705% | Repeating (period 16): 0.0588 to 4 d.p., 5.88% to 2 d.p. | |
| 1/18 | 0.05 | 5.5% | Repeating (period 1): 0.0556 to 4 d.p., 5.56% to 2 d.p. | |
| 1/19 | 0.052631578947368421 | 5.263157894736842105% | Repeating (period 18): 0.0526 to 4 d.p., 5.26% to 2 d.p. | |
| 1/20 | 0.05 | 5% | Exact; 2 decimal places |
A line over digits (like 0.3) marks the block that repeats forever.
| Fraction | Decimal Form | Percentage (%) | Precision String | Copy Row |
|---|---|---|---|---|
| 2/3 | 0.6 | 66.6% | Repeating (period 1): 0.6667 to 4 d.p., 66.67% to 2 d.p. | |
| 3/4 | 0.75 | 75% | Exact; 2 decimal places | |
| 2/5 | 0.4 | 40% | Exact; 1 decimal place | |
| 3/5 | 0.6 | 60% | Exact; 1 decimal place | |
| 4/5 | 0.8 | 80% | Exact; 1 decimal place | |
| 5/6 | 0.83 | 83.3% | Repeating (period 1): 0.8333 to 4 d.p., 83.33% to 2 d.p. | |
| 3/8 | 0.375 | 37.5% | Exact; 3 decimal places | |
| 5/8 | 0.625 | 62.5% | Exact; 3 decimal places | |
| 7/8 | 0.875 | 87.5% | Exact; 3 decimal places | |
| 3/10 | 0.3 | 30% | Exact; 1 decimal place | |
| 7/10 | 0.7 | 70% | Exact; 1 decimal place | |
| 9/10 | 0.9 | 90% | Exact; 1 decimal place | |
| 5/12 | 0.416 | 41.6% | Repeating (period 1): 0.4167 to 4 d.p., 41.67% to 2 d.p. | |
| 7/12 | 0.583 | 58.3% | Repeating (period 1): 0.5833 to 4 d.p., 58.33% to 2 d.p. | |
| 11/12 | 0.916 | 91.6% | Repeating (period 1): 0.9167 to 4 d.p., 91.67% to 2 d.p. | |
| 3/20 | 0.15 | 15% | Exact; 2 decimal places |
| Type | Denominators | Rule | Example | Copy |
|---|---|---|---|---|
| Terminating decimal | 1, 2, 4, 5, 8, 10, 16, 20 | In lowest terms the denominator has only 2 and 5 as prime factors | 1/8 = 0.125 = 12.5% | |
| Repeating decimal | 3, 6, 7, 9, 11, 12, 13, 14, 15, 17, 18, 19 | The denominator has another prime factor: 3, 7, 11, 13, 17 or 19 | 1/7 = 0.142857 | |
| Longest repeating block | 7, 13, 17, 19 | Period lengths: 1/7 = 6, 1/13 = 6, 1/17 = 16, 1/19 = 18 digits | 1/19 = 0.052631578947368421 |
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Frequently Asked Questions
| Question | Answer |
|---|---|
| How do you convert a fraction to a decimal? | Divide the numerator by the denominator. For 3/8: 3 / 8 = 0.375. |
| How do you convert a fraction to a percentage? | Convert the fraction to a decimal and multiply by 100. For 3/8: 0.375 × 100 = 37.5%. |
| What is 1/3 as a decimal and a percentage? | 1/3 = 0.333... (the 3 repeats forever), which is 33.33% to 2 decimal places. Written exactly it is 0.3 and 33.3%. |
| Which fractions give terminating decimals? | A fraction in lowest terms terminates when its denominator has only the prime factors 2 and 5. From 1/1 to 1/20 these are 1/2, 1/4, 1/5, 1/8, 1/10, 1/16, 1/20. All other denominators repeat. |
| What is 1/8 as a decimal and a percentage? | 1/8 = 0.125 = 12.5%. |
| How do you convert a decimal to a fraction? | Write the decimal over a power of 10 and simplify. For 0.75: 75/100 = 3/4. For 0.125: 125/1000 = 1/8. |