Decimal to Fraction
Convert decimal numbers to fractions
Fast, accurate calculations with clear results. Built for speed and ease of use.
Formula
Find GCD and simplifyHow to Use Decimal to Fraction
- Provide your input values.
- Understand the calculation method shown.
- Get immediate and accurate results.
- Use the output for planning or analysis.
Examples
Converting a decimal back to a fraction is the reverse of division, and for any decimal that ends, the method is mechanical: write it over a power of 10 that matches its number of decimal places, then simplify. Repeating decimals need a different trick, since they never end for the power-of-10 method to grab onto.
The formula
fraction = digits after the point / 10^(number of decimal places), then simplify- digits
- the decimal digits written as a whole number
- number of decimal places
- how many digits appear after the decimal point
Worked example
0.375 has three decimal places, so it becomes 375/1000. The greatest common divisor of 375 and 1000 is 125, and dividing both by it gives 3/8, which checks out since 3 divided by 8 is 0.375. A repeating decimal like 0.333... uses algebra instead: let x = 0.333..., then 10x = 3.333..., and subtracting gives 9x = 3, so x = 3/9 = 1/3.
What trips people up
- Skipping the simplification step leaves an ugly but technically correct fraction; 375/1000 and 3/8 are the same value, only one is in lowest terms.
- The repeating-decimal algebra trick needs a different multiplier depending on how many digits repeat; a two digit repeat needs 100x, not 10x.
- A decimal that looks like it repeats but is only rounded for display, such as a calculator screen cutting off at eight digits, is not actually a repeating decimal.
- Negative decimals carry the sign through to the fraction; -0.5 is -1/2, not 1/-2 or an unsigned 1/2.
Frequently asked questions
- What if the decimal has a whole number part, like 2.75?
- Convert only the fractional part, 0.75 becomes 3/4, then add the whole number back, giving 2 and 3/4, or 11/4 written as a single improper fraction.
- How do I simplify a fraction once I have it?
- Find the greatest common divisor of the numerator and denominator and divide both by it; 375/1000 and its GCD of 125 reduce to 3/8.
- Does this method work for a decimal with many places, like 0.0625?
- Yes, the same rule applies regardless of length; 0.0625 has four decimal places, giving 625/10000, which simplifies to 1/16.
- How is a repeating decimal like 0.1666... converted differently from a terminating one?
- It needs the algebraic subtraction method rather than a simple power-of-10 denominator, since a repeating decimal has no finite number of decimal places to build that denominator from.
- Can every decimal be written as a fraction?
- Every terminating or repeating decimal can. An infinite, non-repeating decimal, like the digits of pi, cannot be written as an exact fraction at all, which is what makes it irrational.