Decimal to Fraction Calculator
Type a decimal to get the exact fraction in lowest terms, the mixed number and the working, or round it to the nearest 1/16 for measurements.
- Free
- No sign-up
- Private
For a repeating decimal, put the repeating part in brackets, e.g. 0.(3) or 0.1(6), or end with ...
- Exact fraction
- 3/8
- Mixed number
- 3/8
- Before simplifying
- 375/1000
- Greatest common factor
- 125
- Decimal value
- 0.375
- Percent
- 37.5%
How this was calculated
- 0.375 has 3 digits after the decimal point, so write it over 10^3 = 1000: 375/1000.
- Divide the numerator and denominator by their greatest common divisor, 125: 3/8.
Type a fraction like 5/8 or a mixed number like 2 3/4.
5/8 = 0.625
How to convert a decimal to a fraction
Every terminating decimal is already a fraction in disguise: the digits after the point are tenths, hundredths, thousandths and so on. To convert a decimal to a fraction, write the digits over 1 followed by as many zeros as there are decimal places, then simplify by dividing the top and bottom by their greatest common factor. This decimal to fraction calculator does the same thing with exact whole-number arithmetic, so even a long decimal comes out right, and it shows the unsimplified fraction and the common factor it divided by.
Worked examples
0.375: three decimal places, so 375/1000. The greatest common factor of 375 and 1000 is 125, and 375 ÷ 125 = 3, 1000 ÷ 125 = 8, giving 3/8. 2.125: 2125/1000 simplifies to 17/8, or the mixed number 2 1/8. 0.6: 6/10 = 3/5.
Repeating decimals need one more step. Call the number x. For 0.1666…, multiply by 100 and by 10 so the repeating tails line up: 100x = 16.666… and 10x = 1.666…. Subtracting gives 90x = 15, so x = 15/90 = 1/6. When the whole decimal part repeats, the shortcut is to put the repeating block over the same number of 9s: 0.272727… = 27/99 = 3/11. Type repeating decimals with brackets, such as 0.1(6), or end them with three dots to repeat the last digit.
Rounding to a practical fraction
Some decimals are not meant to be exact. A measurement of 0.33 inches is really "about a third", and a tape measure only shows sixteenths. Choose Nearest 1/n to round to halves, quarters, eighths, sixteenths, thirty-seconds or hundredths: 0.33 × 16 = 5.28, which rounds to 5/16. Choose Simplest close to get the closest fraction under a denominator limit, found with continued fractions. With a limit of 100, 0.333 becomes 1/3, and 3.14159 becomes 311/99; with a limit of 10 it becomes the familiar 22/7.
Common mistakes
- Not simplifying. 50/100 is correct but most teachers want 1/2. The answer here is always in lowest terms.
- Treating 0.333 as 1/3. 0.333 with three digits is exactly 333/1000. Only the repeating decimal 0.333… equals 1/3. Use brackets or "..." to say it repeats.
- Losing the whole number. 1.75 is 7/4 or 1 3/4, not 3/4.
When the result is misleading
A decimal copied from a calculator screen is usually already rounded, so its exact fraction can look strange: 0.6667 is 6667/10000, not 2/3. In that case use "Simplest close". And 0.999… really does equal 1; that is not a rounding error. To find the greatest common factor on its own, use the GCF calculator; to compare two quantities, use the ratio calculator.
Frequently asked questions
How do you convert a decimal to a fraction?
Write the digits after the decimal point over 10, 100, 1000 and so on (one zero per digit), then divide the top and bottom by their greatest common factor. 0.375 = 375/1000, and dividing both by 125 gives 3/8.
How do you convert a repeating decimal to a fraction?
Put the repeating digits over the same number of 9s. 0.333… = 3/9 = 1/3 and 0.142857142857… = 142857/999999 = 1/7. If some digits come before the repeat, as in 0.1666…, the calculator handles that too: it is 1/6.
How do I type a repeating decimal?
Put the repeating part in parentheses, for example 0.(3) for 0.333… or 0.1(6) for 0.1666…, or end the number with three dots to repeat the last digit.
What is 0.625 as a fraction?
5/8. 0.625 = 625/1000, and the greatest common factor of 625 and 1000 is 125.
How do I convert a decimal to the nearest 1/16 inch?
Multiply by 16, round to a whole number and put it over 16, then simplify. 0.33 × 16 = 5.28, which rounds to 5, so the nearest sixteenth is 5/16. Choose "Nearest 1/16" in the calculator.
Key terms
Glossary →- Greatest Common Factor (GCF)
- The greatest common factor (GCF) of two or more positive integers is the largest whole number that divides each of them with no remainder; it is also called the GCD or HCF.