A fraction to percentage table is one of the most useful things you can carry in your head. Once you know that 1/8 is 12.5% or that 1/7 is about 14.29%, a question like "find 12.5% of 640" stops being a multiplication and becomes a quick division. This guide gives you the full table for every unit fraction from 1/1 to 1/20, shows you how each value is worked out, and then gives you a few tricks so you can rebuild any row in seconds instead of memorising twenty separate numbers.
If you are new to percentages, start with our post on quick percentage calculations, which explains that a percentage is simply a number out of 100. This table builds on that idea.
The middle column shows the exact value. Where a decimal goes on forever, the digits in brackets repeat without end, so 33.(3) means 33.333… The last column is rounded to 2 decimal places, which is what you will use most of the time.
| Fraction | Exact percentage | Rounded (2 decimal places) |
|---|---|---|
| 1/1 | 100 | 100% |
| 1/2 | 50 | 50% |
| 1/3 | 33.(3) | 33.33% |
| 1/4 | 25 | 25% |
| 1/5 | 20 | 20% |
| 1/6 | 16.(6) | 16.67% |
| 1/7 | 14.(285714) | 14.29% |
| 1/8 | 12.5 | 12.5% |
| 1/9 | 11.(1) | 11.11% |
| 1/10 | 10 | 10% |
| 1/11 | 9.(09) | 9.09% |
| 1/12 | 8.(3) | 8.33% |
| 1/13 | 7.(692307) | 7.69% |
| 1/14 | 7.1(428571) | 7.14% |
| 1/15 | 6.(6) | 6.67% |
| 1/16 | 6.25 | 6.25% |
| 1/17 | 5.882352… (16-digit cycle) | 5.88% |
| 1/18 | 5.(5) | 5.56% |
| 1/19 | 5.263157… (18-digit cycle) | 5.26% |
| 1/20 | 5 | 5% |
Notice that only seven of these stop: 1/2, 1/4, 1/5, 1/8, 1/10, 1/16 and 1/20 (plus 1/1, which is just 100%). The reason is neat. A fraction in its lowest terms gives a decimal that ends only when its denominator has no prime factors other than 2 and 5, because those are the prime factors of 10. Every other denominator in the table, such as 3, 7, 11 or 13, gives a decimal that repeats forever.
The word percent means "per 100" (see Maths Is Fun on percentages), so turning a fraction into a percentage means asking "how many out of 100 is this?" There are three good ways to do it, and the Maths Is Fun conversion page covers them too.
Divide the top by the bottom to get a decimal, then multiply by 100. For 5/8: 5 ÷ 8 = 0.625, and 0.625 × 100 = 62.5, so 5/8 is 62.5%. If dividing decimals feels slow, our guide to quick decimal calculations will help.
This keeps you away from small decimals. For 3/16, multiply the top by 100 to get 300, then divide: 300 ÷ 16 = 18.75, so 3/16 is 18.75%.
When the denominator divides into 100, multiply the top and bottom by the same number. For 3/4, multiply both by 25: 3 × 25 = 75 and 4 × 25 = 100, so 3/4 becomes 75/100, which is 75%.
Every row in the table above is really one division, 1 ÷ n. For more ways to make those divisions quick, read Division Demystified.
When a decimal goes on forever you have to stop somewhere, and the way you stop matters. The rule from Maths Is Fun's rounding guide is simple: look at the first digit you are dropping. If it is 5 or more, add 1 to the last digit you keep. If it is 4 or less, leave the last digit as it is.
Simply cutting off the digits (chopping) always makes the answer a little too small. Rounding keeps you as close as possible to the true value.
Doubling the denominator halves the fraction, so it also halves the percentage. That means you only need to learn the first value in each chain.
One more shortcut: 1/15 is one third of 1/5. Since 1/5 is 20%, work out 20 ÷ 3, which is 6.666…, so 1/15 is 6.67%.
Any number of ninths (up to 8/9) is a single repeating digit. 1/9 is 11.11%, 2/9 is 22.22%, 4/9 is 44.44%, and 5/9 is 55.555…%, which rounds to 55.56%.
1/11 is 9.0909…%, and the other elevenths are just multiples of the repeating pair 09. So 2/11 is 18.18%, 3/11 is 27.27% and 5/11 is 45.45%. A quick check: 9 × 5 = 45, and the pattern 45.45 follows.
This is the most beautiful pattern in the table. 1/7 as a decimal is 0.142857142857…, and every other seventh uses the same six digits, 142857, just starting at a different place:
| Fraction | Decimal | Percentage (2 decimal places) |
|---|---|---|
| 1/7 | 0.142857… | 14.29% |
| 2/7 | 0.285714… | 28.57% |
| 3/7 | 0.428571… | 42.86% |
| 4/7 | 0.571428… | 57.14% |
| 5/7 | 0.714285… | 71.43% |
| 6/7 | 0.857142… | 85.71% |
How do you know where to start? Multiply the top number by 14 and look for the place in the cycle that begins with digits close to that. For 3/7: 3 × 14 = 42, so 3/7 starts 42.857…, and you carry on round the cycle. For 6/7: 6 × 14 = 84, and the nearest start in the cycle is 857142, so 6/7 is 85.71%.
These three don't belong to a tidy chain, so anchor each one to a neighbour you already know.
To check a value, multiply it back by the denominator. You should get very close to 100:
The answers aren't exactly 100 because the percentages are rounded. In fact 1/17 repeats in a cycle of 16 digits and 1/19 in a cycle of 18 digits, so for mental work two decimal places are plenty. Readers who enjoy working these out by hand can try the techniques in our Vedic maths division tricks.
Here is where the table pays off. When you see a percentage from the table, swap it for its fraction and divide.
You can also use complements. Since 1/6 is 16.67%, 5/6 is the rest of the whole: 100 − 16.67 = 83.33, so 5/6 is 83.33%. In the same way, 100 − 12.5 = 87.5, so 7/8 is 87.5%.
Each of these answers is exact when you use the fraction. Multiplying 350 by 14.29% would give 50.015, which is close but not quite right, while 350 ÷ 7 gives exactly 50. That is why the fraction is both faster and more accurate than the rounded percentage.
You don't need long sessions. Five focused minutes a day for a week is enough to make most of the table automatic.
Each day, cover the percentage column, say each value aloud, then uncover it to check. Mistakes are useful: they show you exactly which rows need another look.
When the values feel familiar, build speed with timed questions. Use the practice page for steady drills and the against time mode to work under exam-style pressure. Since every value in the table comes from a division, strong recall of the 7, 8, 12 and 16 times tables helps a lot, and the times tables chart is a good place to brush up. Be patient with yourself: a little each day adds up quickly.
1/7 is 14.285714…%, with the digits 285714 repeating forever. Rounded to 2 decimal places it is 14.29%.
Rounded to 2 decimal places, 1/6 is 16.67%. The exact value is 16.666…%, and because the first digit dropped is 6, you round up rather than chop to 16.66%.
From 1/2 to 1/20, only 1/2, 1/4, 1/5, 1/8, 1/10, 1/16 and 1/20 give exact values. Their denominators have no prime factors other than 2 and 5; all the others repeat forever.
Multiply the top by 100 and then divide by the bottom, so 3/16 becomes 300 ÷ 16, which is 18.75%. If the bottom divides into 100, scale it up instead, as with 3/4 becoming 75/100.
Learn a few anchors and rebuild the rest: halving chains (1/2, 1/4, 1/8, 1/16), the ninths and elevenths patterns, and the 142857 cycle for sevenths. Five minutes of daily recall with the table covered will lock them in.
These exams are timed and include many percentage questions. Knowing that 12.5% is 1/8 or 14.29% is 1/7 turns a long multiplication into a short division, which saves time and avoids rounding errors.