Fraction to decimal: just divide
Every fraction is a division waiting to happen. The line in the middle literally means "divided by".
So 3/8 is 3 ÷ 8 = 0.375, and multiplying by 100 turns it into a percentage, 37.5%. That is the entire method, whatever the fraction. On paper you would use short or long division; here you type the top and bottom numbers and the decimal appears as you type, along with the percentage equivalent. The only wrinkle is that some divisions never finish, which is where recurring decimals come in below.
Decimal to fraction: place value, then simplify
Going the other way, write the decimal digits over the matching power of ten and cancel down. 0.35 is 35/100, both divide by 5, giving 7/20. For recurring decimals typed in as rounded numbers, the converter searches for the closest fraction with a denominator up to 10,000, so 0.333333 comes back as 1/3 rather than 333,333 over a million. Whole-number parts survive the trip intact: 1.75 splits into 1 and 0.75, giving 7/4, or 1 3/4 as a mixed number.
Why some fractions recur
Our number system is base ten, and ten factorises as 2 × 5. A fraction terminates only if its simplified denominator is built entirely from those two primes: 2, 4, 5, 8, 10, 16, 20 and so on all give tidy decimals. Bring in any other prime factor and the division falls into a loop. 1/3 repeats a single digit forever, while 1/7 = 0.142857142857... cycles through the same six digits endlessly. The converter flags these as recurring and rounds them to six decimal places.
Note that simplifying comes first. 6/8 looks like it contains a troublesome factor, but it reduces to 3/4, so it terminates at 0.75. In maths lessons recurring decimals are written with a dot over the repeating digit, or over the first and last digits of a repeating block, which is why you may see 1/3 written as 0.3 with a dot above the 3.
Common fractions worth memorising
A handful of conversions cover most everyday situations, from splitting bills to reading drill sizes:
- 1/2 = 0.5
- 1/3 ≈ 0.333
- 1/4 = 0.25
- 1/5 = 0.2
- 1/8 = 0.125
- 2/3 ≈ 0.667
- 3/4 = 0.75
- 3/8 = 0.375
- 5/8 = 0.625
- 7/8 = 0.875
- 1/16 = 0.0625
Notice the eighths family: once you know 1/8 = 0.125, the rest are just multiples: 3/8 is three lots of 0.125 and 5/8 is five. Eighths and sixteenths turn up constantly in imperial measurements, from spanner and drill bit sizes to timber thicknesses, so being able to jump between 5/8 inch and 0.625 without reaching for a pencil is genuinely handy in a shed. And if you need to do arithmetic on fractions before converting them, our fraction calculator handles adding, subtracting, multiplying and dividing with simplified answers.
Frequently asked questions
How do I turn a fraction into a decimal?
Divide the top number by the bottom number. So 3/8 is 3 ÷ 8 = 0.375, and 7/16 is 7 ÷ 16 = 0.4375. Multiply the decimal by 100 if you want it as a percentage.
How do I turn a decimal into a fraction?
Write the digits after the point over the matching power of ten, then simplify. For example 0.35 is 35/100, and dividing top and bottom by 5 gives 7/20. The converter does the simplifying for you.
What happens with recurring decimals?
Some fractions never stop, such as 2/3 = 0.6666 recurring, so the tool rounds the decimal to 6 places and tells you it recurs. Going the other way, it finds the closest fraction with a denominator up to 10,000, so typing 0.333333 returns 1/3 rather than an ugly six-figure fraction.
Which fractions give exact decimals?
A fraction terminates only when its simplified denominator is built purely from the factors 2 and 5. That is why halves, quarters, fifths, eighths and tenths are tidy, while thirds, sixths, sevenths and ninths recur forever.
How accurate is the decimal to fraction mode?
If your decimal matches a fraction exactly, you get that fraction and it is labelled exact. Otherwise the tool returns the closest fraction it can find with a denominator up to 10,000 and labels it as approximate, showing the decimal it actually equals.