How to Convert a Fraction to a Decimal and a Percentage, Step by Step

Introduction

Try it now: use our free Fraction to Decimal Converter to get the answer in seconds.

“What is 7 out of 10 as a percentage?” my nephew asked, holding up a spelling test. That one is easy — 70%. Then he flipped the page: 13 out of 20. Then, worse, a recipe his sister was scaling down that called for 5/8 of a cup. Three questions, all secretly the same question, and only the first one felt easy.

Fractions, decimals and percentages are three ways of writing the same amount. A half can be 1/2, 0.5 or 50%, and nothing about the quantity changes — only the costume does. Once you see that converting between them is just changing the costume, the whole topic gets smaller. There is really one division sum at the heart of it, and this guide walks through it slowly, with numbers from tests, kitchens and shop windows rather than a textbook page.

Step one: fraction to decimal is just division

A fraction is a division sum that nobody has finished yet. The line in 3/4 means “3 divided by 4”.

Decimal = numerator ÷ denominator

The numerator is the top number. The denominator is the bottom one. Top divided by bottom — that is the entire method.

Take 3/4:

Divide 3 by 4. It does not go evenly, so add a decimal point and zeros: 3.00 ÷ 4
4 goes into 30 seven times (28), remainder 2
Bring down another zero: 20 ÷ 4 = 5
Answer: 0.75

A few worth knowing by sight, because they turn up everywhere:

1/2 = 0.5
1/4 = 0.25 and 3/4 = 0.75
1/5 = 0.2, 2/5 = 0.4, and fifths simply climb by 0.2
1/10 = 0.1, and tenths are the friendliest of all
1/3 = 0.333… — it never ends, so we write 0.33 and accept the rounding
1/8 = 0.125, which is why that 5/8 cup is 0.625 of a cup

If the top number is bigger than the bottom — 7/4, say — do not let it throw you. 7 ÷ 4 = 1.75. A decimal above 1 simply means the amount is more than one whole thing. Nothing has gone wrong.

Step two: decimal to percentage, move and multiply

Percentage means “out of a hundred”, and the conversion from a decimal is the shortest in all of school maths:

Percentage = decimal × 100

So 0.75 × 100 = 75%. In practice, you slide the decimal point two places to the right and add the % sign. 0.5 becomes 50%. 0.07 becomes 7% — watch that one, because 0.07 is seven hundredths, not seventy of anything.

Going backwards, divide by 100: 40% is 0.4, and 125% is 1.25.

The full journey: 13 out of 20, start to finish

Back to that test score. 13/20 as a percentage, in two steps:

Decimal: 13 ÷ 20 = 0.65
Percentage: 0.65 × 100 = 65%

There is also a shortcut for friendly denominators. If the bottom number divides neatly into 100, scale the fraction up instead. Twentieths are easy: multiply top and bottom by 5 and 13/20 becomes 65/100, which you can read straight off as 65%. Tenths, quarters (×25) and fifths (×20) all work this way. Thirds and sixths do not, so for those, stick with the division method.

Sales use the same maths in disguise. A jacket reduced by 3/8 of its price: 3 ÷ 8 = 0.375, so the discount is 37.5%. On an £80 jacket that is £30 off, £50 to pay. Shops round these numbers for their posters, but now you can check them.

Mistakes we see again and again

Dividing the wrong way round. 4 ÷ 5 is 0.8, so 4/5 is 80%. But 5 ÷ 4 is 1.25. If your decimal for a proper fraction — top smaller than bottom — comes out above 1, you have almost certainly flipped the sum. That built-in check catches the error instantly.

Moving the decimal point one place instead of two. 0.45 is 45%, not 4.5%. Count the jumps out loud if you need to: 0.45 → 4.5 → 45.

Reading 0.5% as a half. Half is 50%, written as a decimal 0.5. 0.5% is half of one percent — a tiny amount, the sort of figure banks use for interest tweaks. The % sign changes the meaning, so do not drop it from your working.

Panicking at endless decimals. 2/3 = 0.666… and 66.7% is a perfectly good answer for anything outside an exam that demands 66.6 recurring. Round to one or two decimal places and say so.

Adding fractions by adding tops and bottoms when converting recipes. 1/2 + 1/4 is not 2/6. Convert each to decimals — 0.5 + 0.25 = 0.75 — and you land on 3/4 without the fraction gymnastics. For cooking, this workaround is honestly easier than the formal method.

Asked at our kitchen table, more or less word for word

“If I got 17 out of 25, is that a pass?”

17 ÷ 25 = 0.68, so 68%. Whether that passes depends on the test, but the conversion is solid — and scaling helps here too, since 25 × 4 = 100, making it 68/100 directly.

Why does my calculator say 1/3 is 0.3333333 but my teacher writes 33.3%?

You are both rounding the same endless number at different lengths. 0.333… × 100 = 33.333…%, which becomes 33.3% at one decimal place. Neither answer is the exact value; the exact value is the fraction itself.

“Can a percentage be bigger than 100? That sounds wrong.”

It sounds wrong but happens whenever something grows beyond its starting size. A plant that was 40 cm and is now 50 cm has grown to 125% of its old height. Percentages above 100 just mean “more than the whole thing we started with”.

Conclusion

One division — top number divided by bottom number — turns any fraction into a decimal, and one multiplication by 100 turns that decimal into a percentage. Keep the sanity checks close: proper fractions give decimals under 1, and the decimal point moves two places, never one. Practise on the next test score, discount or recipe that crosses your table, and within a week the conversions stop needing a guide at all.

Quick conversion table

Fraction	Decimal	Percentage
1/8	0.125	12.5%
1/4	0.25	25%
1/3	0.3333	33.33%
3/8	0.375	37.5%
1/2	0.5	50%
5/8	0.625	62.5%
2/3	0.6667	66.67%
3/4	0.75	75%
7/8	0.875	87.5%
1/1	1	100%