qcalculate

Decimal to Fraction Calculator

Turn any decimal into a fraction in lowest terms, including repeating decimals like 0.333… and 0.1666…, and see each step worked out with your number.

For a repeating decimal, type the digits that repeat in their own box, or write 0.1666… or 0.1(6).

As a fraction

3/4

0.75 = 3/4 as a fraction, or 75% as a percent.

Fraction
3/4
Decimal
0.75
Percent
75%

Show me how

All steps as text

    Tip: press ← and → to move between steps, or click any step.

    How to convert a decimal to a fraction

    1. Count the decimal places. 0.75 has 2.
    2. Write the digits over 1 followed by that many zeros. 0.75 = 75/100. The last digit is in the hundredths place, so 0.75 is 75 hundredths.
    3. Simplify. Divide the top and the bottom by their greatest common divisor, 25: 75/100 = 3/4.
    4. For a decimal bigger than 1, you can also write the answer as a mixed number: 2.125 = 2125/1000 = 17/8 = 2 1/8.

    Worked example: 0.625

    0.625 has 3 decimal places, so 0.625 = 625/1000. The greatest common divisor of 625 and 1000 is 125, and 625 ÷ 125 = 5, 1000 ÷ 125 = 8, so 0.625 = 5/8. Check: 5 ÷ 8 = 0.625.

    Repeating decimals to fractions

    A repeating decimal never ends, so it can’t go over 10, 100 or 1000. A little algebra does the job instead. For 0.1666…, where the 6 repeats:

    1. Call the number x: x = 0.1666…
    2. Multiply by 10 to move past the 1, which doesn’t repeat, and by 100 to move past one 6 as well: 10x = 1.666… and 100x = 16.666…
    3. Subtract. The repeating tails cancel: 100x − 10x = 16 − 1, so 90x = 15.
    4. Divide and simplify: x = 15/90 = 1/6.

    Shortcut when the digits repeat straight after the point: put the repeating block over the same number of 9s. 0.333… = 3/9 = 1/3, 0.2727… = 27/99 = 3/11, and 0.142857142857… = 142857/999999 = 1/7.

    To enter a repeating decimal above, type the repeating digits in their own box (0.1 with 6 repeating), or write 0.1666… or 0.1(6).

    Is 0.999… equal to 1?

    Yes, exactly. The same method gives 10x − x = 9.999… − 0.999… = 9, so 9x = 9 and x = 1. Another way to see it: 1/3 = 0.333…, and three times each side gives 1 = 0.999…

    Common decimals as fractions

    DecimalFractionDecimalFraction
    0.11/100.51/2
    0.1251/80.63/5
    0.21/50.6255/8
    0.251/40.666…2/3
    0.33/100.77/10
    0.333…1/30.753/4
    0.3753/80.84/5
    0.42/50.8757/8

    Decimal inches to fractions

    Tape measures, rulers and drill bits use fractions of an inch, usually down to sixteenths:

    InchesFractionInchesFraction
    0.06251/160.56259/16
    0.1251/80.6255/8
    0.18753/160.687511/16
    0.251/40.753/4
    0.31255/160.812513/16
    0.3753/80.8757/8
    0.43757/160.937515/16
    0.51/211

    For a decimal that isn’t an exact sixteenth, multiply by 16 and round to the nearest whole number: 0.3 × 16 = 4.8, so 0.3 inches is about 5/16.

    Questions

    How do you turn a decimal into a fraction?

    Write the digits over 1 followed by as many zeros as there are decimal places, then simplify: 0.45 = 45/100 = 9/20.

    How do you convert a repeating decimal to a fraction?

    Call it x, multiply it by powers of 10 so that two copies have the same digits after the point, and subtract to cancel the repeating part. Then divide and simplify. Press Play under Show me how to watch it done with your number.

    What is 0.3 as a fraction?

    0.3 = 3/10. The repeating decimal 0.333…, with the 3s going on forever, is 1/3.

    Why does 0.3333 give 3333/10000 and not 1/3?

    Because 0.3333 stops after four 3s, so it is exactly 3333/10000, a little less than 1/3. Only 0.333… with the 3s going on forever equals 1/3. Mark the repeating digit to get 1/3.

    Can every decimal be written as a fraction?

    Every decimal that ends or repeats can. Decimals that go on forever without repeating, like π = 3.14159… or √2 = 1.41421…, are irrational: no fraction equals them exactly. 22/7 is only close to π.