Decimal to fraction converter
Type a decimal to get the simplified fraction, the mixed number and the steps. For a repeating decimal, put the repeating digits in brackets: 0.(3) is 0.333…, 0.1(6) is 0.1666…
Working
- There are 3 digits after the decimal point, so the last digit is in the thousandths place. Write the digits over 1000.
0.375 = 375/1000 - Simplify by dividing top and bottom by the GCF, 125.
375/1000 = 3/8
Place value does the converting for you
Each place after the point is ten times smaller: tenths, hundredths, thousandths. The last digit's place gives the denominator. For 0.375 there are 3 decimal places, so the denominator starts as 1000.
Then simplify: divide top and bottom by the biggest number that goes into both. Repeating decimals need an extra trick (multiply by a power of 10 and subtract), which the working above shows.
How to convert a decimal to a fraction
- Count the digits after the decimal point. 0.625 has three.
- Write the digits without the point over 1 followed by that many zeros: 625/1000.
- Simplify by the greatest common factor (125): 625/1000 = 5/8.
- If there's a whole-number part, keep it: 2.625 = 2 5/8 = 21/8.
Repeating decimals to fractions
A decimal whose digits repeat forever is still an exact fraction. For 0.1666… (written 0.1(6)): let x = 0.1666…. Then 100x = 16.666… and 10x = 1.666…. Subtracting, 90x = 15, so x = 15/90 = 1/6.
A shortcut for pure repeats: the repeating block over as many 9s as it has digits. 0.(7) = 7/9, 0.(27) = 27/99 = 3/11, 0.(142857) = 142857/999999 = 1/7.
Decimals to inch fractions
Tape measures and drill charts use halves, quarters, eighths, sixteenths and so on. The converter rounds to the nearest 1/16" and 1/64" — 0.3 inches is closest to 5/16" (0.3125). The fraction chart lists every sixteenth and its decimal, and the decimal lookup has an answer page for common values.
Questions people ask
How do you convert a decimal to a fraction?
Write the digits after the decimal point over 10, 100, 1000… (one zero per decimal place), then simplify. 0.375 = 375/1000 = 3/8.
What is 0.375 as a fraction?
0.375 = 375/1000. The GCF of 375 and 1000 is 125, so it simplifies to 3/8.
How do I convert a repeating decimal like 0.333… to a fraction?
Type it with the repeating part in brackets, e.g. 0.(3) or 0.1(6). Algebraically: let x = 0.333…, then 10x = 3.333…, subtract to get 9x = 3, so x = 1/3.
What is 0.2 as a fraction?
0.2 = 2/10 = 1/5.
What is 1.25 as a fraction?
1.25 = 125/100 = 5/4, or 1 1/4 as a mixed number.
Can every decimal be written as a fraction?
Every terminating or repeating decimal can. Decimals that never end and never repeat, like π or √2, are irrational and cannot be written exactly as a fraction.