Decimal to Fraction: A Friendly Guide
Convert terminating decimals into fractions and simplify the result.
Quick Answer
a terminating decimal with n decimal places = integer digits / 10ⁿWhen to Use This
A terminating decimal represents a whole number of tenths, hundredths or another power-of-ten unit. Converting it to a fraction makes the value exact and can reveal a simple ratio. Do not treat a rounded decimal as if it were an infinitely repeating value.
Step-by-Step Method
- Count the digits after the decimal point.
- Use 10 raised to that count as the denominator.
- Remove the decimal point to form the numerator, preserving the sign.
- Reduce the fraction by common factors.
Calculator Tips and Limits
- Enter the finite decimal in the linked converter.
- If you intend a repeating decimal, write the repeating pattern separately and use algebra; a finite input has a different exact value.
Worked Examples
Three decimal places
0.375 = 375/1000. Dividing both parts by 125 gives 3/8. Verify by dividing 3 by 8: the result is exactly 0.375.
A value above one
1.25 = 125/100 = 5/4 = 1 1/4. The integer part is included in the numerator; writing only 25/100 would discard the whole 1.
Common Mistakes
Choosing the wrong power of ten
0.375 has three places, so its initial denominator is 1000, not 100.
Calling 0.333 exactly one third
The finite decimal is 333/1000. The infinitely repeating 0.333… is 1/3. Rounding and exact equality are different.
FAQ
Do trailing zeros change the answer?
No. 0.50 = 50/100 = 1/2, the same value as 0.5 = 5/10.
How can a repeating decimal become a fraction?
For x = 0.333…, subtract x from 10x: 9x = 3, so x = 1/3. This relies on the infinite repetition being specified.
References and corrections
OpenStax: Prealgebra 2e — further reading. The worked examples on this page are CalcSolver explanations. Read our calculation and correction method, or report an error with the input and expected result.