Why does the denominator limit matter?
It decides how complex the answer may be. A smaller limit gives a simpler fraction, while a larger limit can match the decimal more closely.
Decimal to Fraction Calculator
Convert a decimal into the cleanest reduced fraction that fits a chosen denominator limit, showing when the result is exact and when it is an approximation.
Control the denominator, control the tradeoff
The calculator searches for the closest reduced fraction within your denominator limit. A smaller limit gives a simpler fraction; a larger limit can match the decimal more closely.
How to choose a denominator limit
- Use 10 for tenths.
- Use 100 for cents or percentages.
- Use 1000 for three-decimal measurements.
- Use 10000 or more when precision matters more than readability.
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Decimal approximation rules
Terminating decimals can often be exact. Repeating and long decimals may depend on the denominator limit.
Approximation search
Simplified result
Error check
Terminating decimal
Repeating decimal
Exact, approximate, or repeating?
Read the result with the denominator limit in mind. A close approximation can be useful, but it is different from an exact conversion of a terminating or recognized repeating decimal.
Common examples
- 0.125 = 1/8.
- 0.333... = 1/3.
- 3.14159 can approximate to 355/113 when the denominator limit allows it.
FAQ
Are repeating decimals converted exactly?
They can be exact when the repeating pattern is recognized and the needed denominator is allowed. Otherwise, the calculator returns the closest simplified fraction within the limit.
