How do you convert a fraction to a percent?

Percent means "per hundred". A percent is a fraction that has agreed to always use 100 as its denominator, so converting a fraction to a percent is one question asked politely: how many would this be out of 100? There are three ways to answer it. They always agree, and which one is fastest depends entirely on the denominator.

Method 1: divide, then multiply by 100

This works on every fraction ever written. The fraction bar means divide, so do the division, then shift the decimal point two places to the right:

3/8    3 ÷ 8    =  0.375     × 100  =  37.5%
5/16   5 ÷ 16   =  0.3125    × 100  =  31.25%
7/40   7 ÷ 40   =  0.175     × 100  =  17.5%
1/250  1 ÷ 250  =  0.004     × 100  =  0.4%

The first half of that is just converting a fraction to a decimal, which has its own post, long division included. The second half is where people slip. The last row is the usual victim: 0.004 is 0.4%, not 4%. Two places, every time, even when the result looks too small to be a respectable percentage.

Method 2: scale the denominator to 100

If the denominator divides 100, skip the division. Multiply the top and the bottom by whatever turns the bottom into 100, and the top is your percent:

7/20   ×  5/5    =  35/100  =  35%
3/25   ×  4/4    =  12/100  =  12%
9/50   ×  2/2    =  18/100  =  18%
3/4    × 25/25   =  75/100  =  75%
3/5    × 20/20   =  60/100  =  60%

works for denominators 2, 4, 5, 10, 20, 25 and 50

Scaling also runs downhill. 45/300 looks unpleasant until you divide both halves by 3 and get 15/100, which is 15%. A denominator that is a multiple of 100 often gives up this way.

It pays to simplify first, because a denominator that does not divide 100 sometimes reduces to one that does. 42/60 is going nowhere as written. Divide both halves by 6 and it is 7/10, which is 70%.

Method 3: multiply by 100 first, then divide

Same arithmetic as Method 1 in the opposite order, and the better choice when you have no calculator. Multiplying the numerator by 100 is free (write two zeros), and it leaves you one whole number division:

3/8    300 ÷ 8  =  37.5%

5/6    500 ÷ 6  =  83 remainder 2
                =  83 2/6%
                =  83 1/3%          about 83.33%

2/7    200 ÷ 7  =  28 remainder 4
                =  28 4/7%          about 28.57%

Notice what the remainder did. It went over the original denominator and became a small fraction on the end of the percent, the same move as turning an improper fraction into a mixed number. That gives an exact answer where the decimal route can only offer a rounded one.

When the division never ends

If the reduced denominator has any prime factor other than 2 or 5, the decimal repeats forever and so does the percent. The classics:

1/3  =  33.333...%   =  33 1/3%
2/3  =  66.666...%   =  66 2/3%
1/6  =  16.666...%   =  16 2/3%
1/9  =  11.111...%   =  11 1/9%

For a test score or a headline, round it and move on: 33.33% is fine. For anything that still has arithmetic ahead of it, the rounding is a small debt that comes due later:

33.33%  × 3   =  99.99%       a hundredth of a percent has gone missing
33 1/3% × 3   =  100%         exactly

Three equal shares of anything should add up to all of it. This is the same leak that makes averaging percentages treacherous, and it is why a three way split written as 33.33% each never quite covers the bill.

Scores, which is why most people are here

A score is a fraction wearing a different hat. Points earned on top, points available on the bottom:

17 out of 20   =  17/20  × 5/5   =  85/100  =  85%
42 out of 60   =  42/60  =  7/10            =  70%
23 out of 30   =  2300 ÷ 30  =  76.666...   =  76.67% rounded

The first scales, the second simplifies, the third needs the division. If you would rather start from the question "what percent is this of that", the percentage post covers the same ground from the other side.

Fractions bigger than 1 go past 100%

Nothing changes. An improper fraction is more than one whole, so its percent is more than 100, and that is correct rather than alarming:

5/4      5 ÷ 4   =  1.25    =  125%
7/2      7 ÷ 2   =  3.5     =  350%
1 1/2    =  3/2  =  1.5     =  150%
2 3/8    =  19/8 =  2.375   =  237.5%

For a mixed number you can also convert the pieces separately: the whole number is that many hundreds, and the fraction is whatever it would be alone. 2 3/8 is 200% plus 37.5%.

The fractions worth knowing by heart

You only need the unit fractions. Every eighth is 12.5%, so 5/8 is five of them, 62.5%. Every sixteenth is 6.25%, every twentieth is 5%, every twenty-fifth is 4%. The rest of the table is multiplication.

Going back: percent to fraction

Put the percent over 100 and reduce. If there is a decimal in the percent, multiply both halves by 10 until it is gone:

35%      =  35/100                 =  7/20     divide both by 5
150%     =  150/100                =  3/2      divide both by 50
12.5%    =  12.5/100  =  125/1000  =  1/8      divide both by 125
33 1/3%  =  100/3 ÷ 100            =  1/3

This is decimal to fraction with the decimal point already moved for you.

Where a calculator gets this wrong

Most software stores numbers in binary floating point, and most fractions have no exact binary form. The division lands a hair off, and multiplying by 100 makes the hair visible. These are real results from JavaScript and Python:

11 / 20 * 100    =  55.00000000000001     should be 55
29 / 50 * 100    =  57.99999999999999     should be 58

1 / 3 * 100      =  33.33333333333333
100 / 3          =  33.333333333333336    same sum, two answers

Eleven twentieths is 55%. Not roughly, not to fourteen decimal places. It is the same fault that makes 0.1 + 0.2 miss 0.3, and the usual patch is to round the display and hope. Prism does the arithmetic on exact rationals instead, so 11/20 × 100 is 55, 0.1 + 0.2 is exactly 0.3, and 1/3 × 100 stays 100/3 until you ask for a decimal.

Type 3/8 × 100 and read 37.5

Prism's fraction mode computes exactly, so 1/3 × 100 comes back as 100/3, not 33.33333333333333. For scores, the percentages tool takes a Part and a Whole and shows the Share. Fractions and percentages are free forever, no ads, no subscription. See the app.