Decimal to Fraction Calculator
Convert a positive or negative terminating decimal to a reduced fraction and mixed number with the place-value steps shown.
Decimal to Fraction Calculator
How it works
Formula and steps
The formula shows how the decimal to fraction calculator turns your inputs into the result. Use it to check the calculation, then follow the example steps to see each part of the math.
Formula & steps
Decimal to fraction formula
Use a power of ten based on the number of digits after the decimal point, then simplify.
integer digits= The entered number without its decimal pointn= Number of digits after the decimal point- 1Enter a terminating decimal.
- 2Use 10, 100, 1,000, or the matching power of ten as the denominator based on the number of decimal places.
- 3Write the decimal digits as the numerator.
- 4Reduce the fraction and show a mixed number when its absolute value is greater than one.
Worked examples
Common uses
- Converting terminating decimals
- Turning measurements into fractions
- Finding a mixed-number equivalent
- Checking exact decimal values
Common mistakes
- Using the wrong power of ten for the denominator.
- Forgetting to reduce the resulting fraction.
- Entering repeating-decimal notation, which this calculator does not support.
Fraction guide
How to convert a decimal to a fraction
A terminating decimal can be written over a power of ten determined by its final decimal place, then reduced to lowest terms.
Use decimal place value
Tenths use denominator 10, hundredths use 100, thousandths use 1,000, and additional places continue with powers of ten.
Reduce and show a mixed number
Divide the numerator and denominator by their greatest common factor. Values above one also receive an equivalent mixed-number result.
Terminating decimals only
The calculator converts the finite digits entered. Repeating bars and ellipsis notation for infinite decimals are not accepted.
FAQ
Write the decimal digits over the matching place value, then divide the numerator and denominator by their greatest common factor.
Yes. A decimal greater than one can be written as an improper fraction and then as an equivalent mixed number.
It converts the finite digits you enter. It does not accept repeating bars or ellipsis notation for infinitely repeating decimals.
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