Decimal to Fraction Calculator
Convert terminating and repeating decimals into simplified fractions and mixed numbers. Enter ordinary decimals such as 0.75 or repeating notation such as 0.(3). The calculator reduces the result automatically and can also show the nearest practical fraction denominator for measurement work.
Repeating decimals can be entered with parentheses, such as 0.(3) or 1.2(34).
How to use the Decimal to Fraction Calculator
- Enter a terminating decimal or use parentheses to identify a repeating group.
- For terminating decimals, the digits are written over the corresponding power of ten.
- For repeating decimals, equivalent shifted equations are used to eliminate the repeating portion.
- The numerator and denominator are divided by their greatest common factor.
- Improper fractions are also displayed as mixed numbers when appropriate.
Examples
0.75
0.75 becomes 75/100 and reduces to 3/4.
1.625
1.625 reduces to 13/8, which is 1 5/8 as a mixed number.
0.(3)
The repeating decimal 0.333... is exactly equal to 1/3.
Frequently asked questions
How do you convert a decimal to a fraction?
Write the decimal digits as an integer over a power of ten, then divide the numerator and denominator by their greatest common factor.
Can repeating decimals be converted exactly?
Yes. Repeating decimals represent rational numbers and can be converted exactly using algebraic subtraction of shifted decimal equations.
What is a mixed number?
A mixed number combines a whole number and a proper fraction, such as 1 5/8.
Does this calculator simplify fractions?
Yes. The fraction is automatically reduced using the greatest common factor.
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