Fraction to Decimal Converter & Calculator
Fractions to decimals and back, simplified, plus the four operations with the working shown.
In short
To convert a fraction to a decimal, divide the numerator by the denominator: 3/8 is 3 ÷ 8 = 0.375. To go the other way, write the decimal over a power of ten and simplify. 0.375 becomes 375/1000, which reduces to 3/8.
Last reviewed
Runs entirely in your browser. Nothing you type here is uploaded, stored or logged.
The four operations
Adding and subtracting needs a common denominator. Convert both fractions so their bottoms match, then add or subtract the tops:
1/4 + 1/6 → 3/12 + 2/12 = 5/12Multiplying is the easy one, tops together, bottoms together, then simplify:
2/3 × 3/4 = 6/12 = 1/2Dividing means flipping the second fraction and multiplying:
1/2 ÷ 1/4 = 1/2 × 4/1 = 4/2 = 2That last one is worth a moment. "How many quarters fit in a half?", two. Division by a fraction smaller than one makes the answer bigger, which looks wrong and isn't.
Simplifying
Divide top and bottom by their greatest common divisor. For 18/24 that is 6, giving 3/4. The tool does this automatically, since an unsimplified answer is technically correct and practically useless.
Where fractions still matter daily
Tape measures and workshops. Imperial measurement runs on halves, quarters, eighths and sixteenths. Drill bits, spanners, timber and pipe are all sized that way, so converting 7/16 to 0.4375 is a routine task rather than a school exercise.
Cooking. American recipes use ⅓ cup and ¾ teaspoon. Halving a recipe that calls for ¾ cup means knowing that's ⅜.
Odds and probability. Betting odds, statistics and risk are all fractional.
Music. Time signatures and note values are fractions. A quarter note is a quarter of a whole.
Recurring decimals
Some fractions never terminate. 1/3 is 0.333… forever, 1/7 is 0.142857 repeating.
The rule is that a fraction terminates only if its simplified denominator has no prime factors other than 2 and 5. Which is why halves, quarters, fifths, eighths and tenths all terminate, and thirds, sixths, sevenths and ninths do not.
This tool marks recurring results rather than presenting a rounded value as exact. That distinction matters when the rounding compounds: 0.33 × 3 is 0.99, not 1.
Converting a decimal back to a fraction
For a terminating decimal, put it over a power of ten and simplify. 0.375 → 375/1000 → 3/8.
For anything else, a measurement, a recurring value, a value with rounding error. The tool finds the closest simple fraction instead, using a continued-fraction search. That gives you 1/3 for 0.3333 rather than the technically exact but useless 3333/10000.
Frequently asked questions
How do I convert a fraction to a decimal?
Divide the top number by the bottom one. 3/8 is 3 ÷ 8 = 0.375. Some fractions do not terminate, 1/3 is 0.333… recurring, and the tool marks those rather than pretending the rounded value is exact.
How do I convert a decimal to a fraction?
Write the decimal over a power of ten and simplify: 0.375 becomes 375/1000, which reduces to 3/8. Recurring decimals need a different method, and the tool finds the closest simple fraction rather than a very large exact one.
How do I add fractions with different denominators?
Convert both to a common denominator, add the numerators, then simplify. For 1/4 + 1/6, the lowest common denominator is 12: 3/12 + 2/12 = 5/12. The working is shown for each calculation.
What is an improper fraction?
One where the numerator is larger than the denominator, like 7/4. It is perfectly valid and often easier to calculate with. The mixed-number form, 1¾, is easier to picture. Both are given.
Why do I need this outside school?
Imperial measurements. Tape measures, spanner sets, drill bits and American recipes all work in halves, quarters, eighths and sixteenths, and converting 7/16 of an inch to a decimal is a genuine daily task in any workshop or kitchen.