Steps without the calculator
For a terminating decimal, remove the decimal point to make the numerator and use 10, 100, 1000, or the appropriate power of ten as the denominator. Then reduce with the GCF.
Math calculator
Decimal to Fraction Calculator
Express a terminating or approximated decimal as a fraction in lowest terms. The page traces how the inputs become reduced fraction before rounding.
Decimal to Fraction inputs
Enter the source values
A worked example
Write 0.375 as 375/1000. Both numbers share a factor of 125; dividing top and bottom by 125 produces 3/8. Dividing 3 by 8 returns 0.375 exactly. This Decimal to Fraction example can be compared with reduce with a GCF.
Situations that fit the model
Fraction form can reveal an exact proportion that a rounded decimal hides. It is handy in measurement, probability, scale drawings, and any calculation where common denominators matter.
Why this relationship works
A terminating decimal is a rational number because it can be placed over a power of ten. For example, three decimal places indicate thousandths, so 0.375 begins as 375/1000 before reduction. For a connected concept in Decimal to Fraction, see mixed-number conversion.
For this page, decimal to fraction is interpreted under the stated convention and input order.
Mistakes worth catching
A decimal copied from a rounded display may only approximate the original fraction. Entering 0.333 gives 333/1000, not exactly 1/3; a longer repeating approximation may be recognized more closely but is still an approximation. If the Decimal to Fraction assumptions do not fit, consider percentage conversion.
Changing only one field helps distinguish a data-entry problem from the intended behavior of decimal to fraction.
Meaning, scale, and reporting
Transfer decimal one at a time and keep their units visible in your notes. This page can validate numerical ranges, but only the reader can confirm that each value represents the intended quantity.
Terminating decimals settle on denominators composed of factors 2 and 5 after reduction. Other displayed decimals may be approximations to fractions with different denominator structures. Trying a nearby input should follow this pattern; otherwise inspect the field assignment.
Attach units and the name reduced fraction whenever the answer leaves this page. A rounded value is suitable for presentation, while retained working digits are safer for a dependent calculation.
This conversion seeks a rational representation, whereas rounding seeks a nearby decimal with fewer places. Those goals differ whenever the entered decimal was itself an approximation. That neighboring measure needs its own setup rather than a relabeled answer.
Copying only the decimal discards the setup. Pair the reduced fraction with decimal and the unit convention so another reader can reconstruct its meaning.
A few useful clarifications
Can every decimal be written as a fraction?
Every terminating or repeating decimal is rational. Nonrepeating, nonterminating decimals such as π are irrational.
Why might the answer be an approximation?
A finite input cannot preserve an unlimited repeating pattern or an irrational value exactly.
How do I check the fraction?
Divide its numerator by its denominator and compare that decimal with the original input.
What happens with a negative decimal?
The fraction keeps the negative sign while its denominator remains positive.