Converting between fractions, decimals and percentages

A fraction, a decimal and a percentage are three ways of writing the same quantity. A half is 0.5 and 50 per cent. A quarter is 0.25 and 25 per cent. Moving between them is something you do all the time without noticing, when you read a 20 per cent discount as one fifth off, or work out that 17 out of 20 is 85 per cent. This guide sets out the rules for converting in each direction, gives a table of the common values worth memorising, and shows worked examples from shopping, cooking and exam marks.

By Valtrinity. Updated 18 October 2026.

The three forms of the same number

A fraction shows a part of a whole as one number over another: 3/4 means three parts out of four. A decimal shows the same part using place value: 0.75 means seven tenths and five hundredths. A percentage shows it out of one hundred: 75 per cent means 75 parts out of 100.

They are interchangeable, and each is better for a different job. Fractions are exact and good for sharing and cooking, such as one third of a cake. Decimals are convenient on a calculator and for money. Percentages make it easy to compare quantities of different sizes, such as a pass mark or an interest rate.

The key idea is that the percentage is just the decimal multiplied by 100, and the decimal is just the top of the fraction divided by the bottom.

Fraction to decimal

Divide the top number, the numerator, by the bottom number, the denominator. 3 divided by 4 is 0.75, so 3/4 is 0.75. 1 divided by 8 is 0.125. 7 divided by 20 is 0.35.

Some fractions never end as decimals. 1/3 is 0.3333 and the threes go on for ever, and 2/3 is 0.6667 when rounded to four places. These are called recurring decimals. When you need a figure for a calculation, round to the number of places that matches the accuracy you need, and keep the fraction itself if you want the exact value.

Mixed numbers work the same way. 2 and 3/5 is 2 plus 3 divided by 5, which is 2.6. A quick check is that the decimal part should be between 0 and 1, and bigger than 0.5 when the fraction is more than a half.

Decimal to percentage and back

To change a decimal into a percentage, multiply by 100, which in practice means moving the decimal point two places to the right. 0.75 becomes 75 per cent. 0.08 becomes 8 per cent. 1.25 becomes 125 per cent.

To change a percentage into a decimal, divide by 100, moving the point two places to the left. 35 per cent becomes 0.35. 6 per cent becomes 0.06, not 0.6, and that slip is one of the most common errors. 120 per cent becomes 1.2.

The decimal form is the one to use for calculation. To find 35 per cent of £80, multiply 80 by 0.35 to get £28. To increase £80 by 35 per cent, multiply by 1.35 to get £108.

Fraction to percentage and back

The simplest route is through the decimal. 7/20 is 0.35, so it is 35 per cent. Alternatively, scale the fraction to a denominator of 100. 7/20 is the same as 35/100, because multiplying the top and bottom by 5 does not change the value, and 35/100 is 35 per cent.

To go from a percentage to a fraction, write it over 100 and simplify. 40 per cent is 40/100. Divide the top and bottom by 20 to get 2/5. 85 per cent is 85/100, and dividing by 5 gives 17/20. 12.5 per cent is 12.5/100, which becomes 125/1000 and then 1/8.

To simplify a fraction, find the largest number that divides both parts exactly. For 40/100 that is 20. If you are not sure, keep dividing by small common factors such as 2, 5 and 10 until you cannot go any further.

Values worth memorising

A handful of conversions come up so often that they are worth knowing by heart. 1/2 is 0.5 and 50 per cent. 1/4 is 0.25 and 25 per cent. 3/4 is 0.75 and 75 per cent. 1/5 is 0.2 and 20 per cent. 1/10 is 0.1 and 10 per cent. 1/8 is 0.125 and 12.5 per cent. 1/3 is 0.333 and 33.3 per cent. 2/3 is 0.667 and 66.7 per cent.

These let you do everyday arithmetic quickly. A 25 per cent discount is a quarter off, so a £60 jacket loses £15. A 20 per cent tip on a £35 meal is a fifth, which is £7. Ten per cent is just the value divided by ten, and 5 per cent is half of that.

If you know 10 per cent, you can build the others. 15 per cent is 10 per cent plus half of it. 30 per cent is three times 10 per cent. For 17.5 per cent, add 10 per cent, 5 per cent and 2.5 per cent.

Worked examples

Exam mark: a student gets 34 out of 40. As a fraction that is 34/40, which simplifies to 17/20. As a decimal it is 0.85. As a percentage it is 85 per cent.

Recipe: a recipe needs 3/8 of a litre of milk and you only have a measuring jug marked in millilitres. 3 divided by 8 is 0.375 litres, which is 375 ml.

Price change: a coat costs £120 and is reduced by 3/10. 3/10 is 0.3, which is 30 per cent. The discount is £36, so the new price is £84. Equivalent routes: multiply £120 by 0.7 to get £84 directly.

Survey: 18 of 24 respondents said yes. 18/24 simplifies to 3/4, which is 0.75, or 75 per cent. Reporting the percentage lets you compare it with another survey of a different size, where 45 out of 60 said yes. 45/60 is also 3/4 and 75 per cent, so the two surveys match.

Mistakes to avoid

A frequent slip is to divide the wrong way round. A fraction such as 3/8 is 3 divided by 8, not 8 divided by 3. A check is that a fraction less than one should give a decimal less than one.

Another is to confuse 1/4 per cent with 1/4. A quarter of a per cent is 0.25 per cent, which is 0.0025 as a decimal. A quarter is 25 per cent, or 0.25. When rates are quoted, such as mortgage rate changes of a quarter of a point, the difference is large.

A last one is rounding too early. 1/3 as 0.33 looks fine, but three lots of 0.33 make 0.99, not 1. If the result will be used in another calculation, keep extra places or work with the fraction until the end.

Tools mentioned in this guide

Frequently asked questions