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Fractions as decimals and percentages

Pick a fraction to see it as a decimal and a percentage, worked out step by step, or turn a decimal or percentage back into a fraction.

Fractions, decimals and percentages chart

Every fraction here is in its simplest form: the top and bottom have no common factor bigger than 1. This is also called lowest terms. Tap a decimal or a percentage to see how it is worked out. A dot over a digit means it repeats for ever.

FractionDecimalPercentage
one half, 0.550%
one third, 0.3, where the 3 repeats for ever33 1/3%
two thirds, 0.6, where the 6 repeats for ever66 2/3%
one quarter, 0.2525%
three quarters, 0.7575%
one fifth, 0.220%
two fifths, 0.440%
three fifths, 0.660%
four fifths, 0.880%
one sixth, 0.16, where the 6 repeats for ever16 2/3%
five sixths, 0.83, where the 3 repeats for ever83 1/3%
one seventh, 0.142857, where the group 142857 repeats for ever14 2/7%
two sevenths, 0.285714, where the group 285714 repeats for ever28 4/7%
three sevenths, 0.428571, where the group 428571 repeats for ever42 6/7%
four sevenths, 0.571428, where the group 571428 repeats for ever57 1/7%
five sevenths, 0.714285, where the group 714285 repeats for ever71 3/7%
six sevenths, 0.857142, where the group 857142 repeats for ever85 5/7%
one eighth, 0.12512.5%
three eighths, 0.37537.5%
five eighths, 0.62562.5%
seven eighths, 0.87587.5%
one ninth, 0.1, where the 1 repeats for ever11 1/9%
two ninths, 0.2, where the 2 repeats for ever22 2/9%
four ninths, 0.4, where the 4 repeats for ever44 4/9%
five ninths, 0.5, where the 5 repeats for ever55 5/9%
seven ninths, 0.7, where the 7 repeats for ever77 7/9%
eight ninths, 0.8, where the 8 repeats for ever88 8/9%
one tenth, 0.110%
three tenths, 0.330%
seven tenths, 0.770%
nine tenths, 0.990%
one eleventh, 0.09, where the group 09 repeats for ever9 1/11%
two elevenths, 0.18, where the group 18 repeats for ever18 2/11%
three elevenths, 0.27, where the group 27 repeats for ever27 3/11%
four elevenths, 0.36, where the group 36 repeats for ever36 4/11%
five elevenths, 0.45, where the group 45 repeats for ever45 5/11%
six elevenths, 0.54, where the group 54 repeats for ever54 6/11%
seven elevenths, 0.63, where the group 63 repeats for ever63 7/11%
eight elevenths, 0.72, where the group 72 repeats for ever72 8/11%
nine elevenths, 0.81, where the group 81 repeats for ever81 9/11%
ten elevenths, 0.90, where the group 90 repeats for ever90 10/11%
one twelfth, 0.083, where the 3 repeats for ever8 1/3%
five twelfths, 0.416, where the 6 repeats for ever41 2/3%
seven twelfths, 0.583, where the 3 repeats for ever58 1/3%
eleven twelfths, 0.916, where the 6 repeats for ever91 2/3%
one sixteenth, 0.06256.25%
three sixteenths, 0.187518.75%
five sixteenths, 0.312531.25%
seven sixteenths, 0.437543.75%
nine sixteenths, 0.562556.25%
eleven sixteenths, 0.687568.75%
thirteen sixteenths, 0.812581.25%
fifteen sixteenths, 0.937593.75%
one twentieth, 0.055%
three twentieths, 0.1515%
seven twentieths, 0.3535%
nine twentieths, 0.4545%
eleven twentieths, 0.5555%
thirteen twentieths, 0.6565%
seventeen twentieths, 0.8585%
nineteen twentieths, 0.9595%
one twenty-fifth, 0.044%
two twenty-fifths, 0.088%
three twenty-fifths, 0.1212%
four twenty-fifths, 0.1616%
one fiftieth, 0.022%
one hundredth, 0.011%

These pages connect fractions, decimals and percentages. Some examples are extra practice beyond the statutory KS2 programme, including recurring decimals, mixed percentages and answers with more than three decimal places. They are not a checklist of what every pupil must learn at a particular age.

Not in its simplest form?

A fraction like 2/4 has no page of its own, because it is the same as 1/2. Find yours here and go to its simplest form.

Decimals as fractions

Percentages as fractions

How the conversions work

A fraction is a division: 3/8 means 3 ÷ 8. Dividing the top by the bottom always gives the decimal, and multiplying the decimal by 100 gives the percentage.

When the bottom goes exactly into 10, 100, 1,000 or 10,000, there is a quicker way: make an equivalent fraction with that bottom. 2/5 = 40/100, so it is 0.4 and 40%. That works for halves, quarters, fifths, eighths, tenths, sixteenths, twentieths, twenty-fifths, fiftieths and hundredths.

Extension: a prime number has exactly two factors, 1 and itself. The prime factors of a number are the primes that multiply to make it; for example, 12 = 2 × 2 × 3. When the bottom of a fraction in its simplest form has a prime factor other than 2 or 5, such as 3, 7 or 11, the division never ends and the decimal recurs: 1/3 = 0.3, where the 3 repeats for ever and 1/7 = 0.142857, where the group 142857 repeats for ever. The dot goes over a single repeating digit, or over the first and last digits of a repeating group.

Try the fraction wall

This wall has rows for halves, thirds, quarters, fifths, sixths, eighths and tenths. Tap a piece to shade a fraction, then look straight down: every row that ends in exactly the same place shows an equivalent fraction. It is a selected model, so some denominators on this site have no row here.

A fraction wall from halves to tenths. Shade a fraction and look straight down to find the equivalent fractions.

Questions parents ask

How do you turn a fraction into a decimal?

Divide the top by the bottom. 3/8 is 3 ÷ 8 = 0.375. When the bottom goes exactly into 10, 100 or 1,000, you can instead make an equivalent fraction with that bottom: 3/8 = 375/1,000 = 0.375.

How do you turn a fraction into a percentage?

Per cent means out of 100. If you can make the bottom 100, the top is the percentage: 2/5 = 40/100 = 40%. Otherwise, find the decimal and multiply by 100: 3/8 = 0.375 = 37.5%.

What is a recurring decimal?

A decimal that never stops, because the same digit or group of digits repeats for ever. 1/3 = 0.333... and 1/7 = 0.142857142857.... One way to show the repeating part is to place a dot over the repeating digit, or over the first and last digits of a repeating group.

Why is 2/4 not on the list?

2/4 is the same as 1/2: divide the top and bottom by 2. Each fraction appears once, in its simplest form, and its page lists the other fractions that are equal to it.

Continue your maths practice

Explore the diagnostic for another way to practise.

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