How Fractions, Decimals and Percentages Relate — A Complete Guide

Half a pizza, 0.5 of a pizza, and 50% of a pizza are not three different amounts. They are the same amount written three different ways. Fractions, decimals and percentages are simply three languages for the same idea: a part of a whole. Once you can move fluently between them, a great deal of everyday maths becomes easier, from reading a test score to comparing two sale prices, because you can always switch to whichever form makes the comparison or calculation simplest.

What each form actually means

A fraction shows a part out of a whole. In 3/4, the bottom number, the denominator, says the whole was split into 4 equal parts, and the top number, the numerator, says you have 3 of them. A decimal writes the same idea using place value: 0.75 means 7 tenths and 5 hundredths, which together are 75 hundredths. A percentage means "out of one hundred": 75% literally means 75 out of 100. That is why 3/4, 0.75 and 75% are equal. The whole is 4/4, 1.0 and 100% in the three forms, and each form is just a different way of counting the same share.

The three conversions, and nothing else

Every conversion between these forms uses one of three moves. To turn a fraction into a decimal, divide the top number by the bottom number: 3 divided by 4 is 0.75. To turn 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%. To turn a percentage into a fraction, write it over 100 and simplify: 75% is 75/100, and dividing the top and bottom by 25 gives 3/4. Every other conversion is just two of these moves chained together. A fraction becomes a percentage by first becoming a decimal, and a percentage becomes a decimal by dividing by 100, which moves the decimal point two places to the left: 75% is 0.75.

Values worth knowing by heart

A small set of conversions comes up so often that memorising them saves real time. One half is 1/2, 0.5 and 50%. One quarter is 1/4, 0.25 and 25%, and three quarters is 3/4, 0.75 and 75%. One fifth is 1/5, 0.2 and 20%, and two fifths is 2/5, 0.4 and 40%. One tenth is 1/10, 0.1 and 10%. One eighth is 1/8, 0.125 and 12.5%, and three eighths is 3/8, 0.375 and 37.5%. If you know these by heart, you can estimate most everyday conversions without reaching for a calculator, and you have a ready check on any answer a calculator gives you.

Worked example 1: a test score in all three forms

Suppose you score 18 out of 24 on a test. As a fraction, that is 18/24. Simplify it by dividing the top and bottom by 6, and you get 3/4. As a decimal, divide 3 by 4 to get 0.75. As a percentage, multiply 0.75 by 100 to get 75%. All three answers describe the same performance, and the percentage is usually the form a teacher reports, because it is the easiest to compare with other scores. A classmate who scored 30 out of 40 also scored 75%, even though the two fractions look different, which is exactly why converting to a common form matters.

Worked example 2: the same calculation three ways

Imagine 35% of a group of 240 people choose a particular option. As a percentage calculation, that is 240 × 35 ÷ 100 = 84. As a fraction, 35% is 35/100, which simplifies to 7/20, and 7/20 of 240 is 7 × 240 ÷ 20 = 84. As a decimal, 35% is 0.35, and 0.35 × 240 = 84. Three routes, one answer. In practice, pick the route that is easiest for the numbers in front of you: the fraction route is often cleanest when the numbers divide neatly, and the decimal route is often quickest on a calculator.

Worked example 3: comparing values in different forms

Which is largest: 3/8, 0.4, or 35%? Comparing them directly is hard, because they are written in different languages. Convert them all to percentages. 3/8 is 3 ÷ 8 = 0.375, which is 37.5%. 0.4 is already a decimal, and multiplying by 100 gives 40%. 35% is already a percentage. Now the comparison is easy: 40% is the largest, then 37.5%, then 35%. The rule is simple and general: when values arrive in mixed forms, convert them all to one form before comparing. Percentages are usually the best common form, because they are built for comparison.

The awkward case: repeating decimals

Not every fraction converts neatly. One third is 1 ÷ 3 = 0.333..., with the 3 repeating forever, so as a percentage it is 33.333...%. In practice we round it, usually to 33.3%. Two thirds is 0.666... and 66.7% rounded. Here a small honesty point matters: 33.3% plus 66.7% is 100%, but 33.333...% plus 66.666...% is also 100%, while the rounded figures 33.3% and 66.7% add to exactly 100% only by luck of the rounding. When you round, say so, and do not be surprised if rounded parts add to 99.9% or 100.1%. The underlying fractions are exact; the decimals are approximations.

Common mistakes to avoid

First, do not confuse 0.5 with 0.5%: 0.5 as a decimal is 50%, while 0.5% is only 0.005 as a decimal, one hundred times smaller. The percent sign changes everything. Second, do not move the decimal point the wrong way: converting a decimal to a percentage moves it right, and converting a percentage to a decimal moves it left. Third, do not forget to simplify: 75/100 is correct, but 3/4 is the finished answer, and exam markers and readers expect it. Fourth, remember that percentages can exceed 100%: 150% means one and a half wholes, or 1.5 as a decimal and 3/2 as a fraction. That happens whenever a quantity grows beyond its original size, for example when a price rises by half again.

Frequently asked questions

Why do we need three forms at all?

Because each form is convenient in a different situation. Fractions are exact and easy to simplify, decimals are easy to type into a calculator and to add, and percentages are easy to compare. Being able to switch means you are never stuck with an awkward form.

Is 0.25 the same as 25%?

Yes. 0.25 × 100 = 25, so 0.25 and 25% are the same value. The decimal 0.25 without a percent sign is 25 hundredths; with the sign, 25% means 25 out of 100, which is the same thing.

How do I convert a percentage back to a fraction quickly?

Write the percentage over 100 and simplify. 40% is 40/100, which simplifies to 2/5. 12.5% is 12.5/100, which is 125/1000, simplifying to 1/8. If the percentage has a decimal in it, clear the decimal first by multiplying the top and bottom by 10.

Can a fraction be bigger than 1?

Yes. A fraction whose top number is larger than its bottom number, such as 5/4, is bigger than a whole: 5/4 is 1.25 and 125%. It simply means one whole plus an extra quarter.

Try it yourself with the Percentage Calculator, and for the general percentage method, read How to Calculate a Percentage and How Discounts and Sale Prices Work.