Math & Scientific
Decimal to Fraction Formula: Place Value and Reduction
Turn a finite decimal into an exact fraction, reduce it with a greatest common divisor, and distinguish written digits from an intended repeating decimal.
Use the number of written decimal places
A finite decimal can be written as an integer divided by a power of ten. If the decimal has k places after the point, remove the point to form the numerator and use 10 to the power k as the denominator. For example, 0.625 has three decimal places, giving 625/1000. The leading zero before the point does not add a decimal place. This construction is exact for the number as written; it does not guess whether the decimal was originally rounded from a different value.
Reduce both parts by the same factor
The greatest common divisor of 625 and 1000 is 125. Dividing both numerator and denominator by 125 gives 5/8. Dividing only the numerator would change the value rather than simplify it. A useful check is 5×125=625 and 8×125=1000, showing that the original and reduced fractions describe the same ratio. You can also divide 5 by 8 to reconstruct 0.625. Reduction changes the representation of the number, not its magnitude or its original precision as a measurement.
Include the whole-number part in the numerator
For 1.875, removing the decimal point gives 1875, not 875. The initial fraction is 1875/1000, which reduces to 15/8. Dividing fifteen by eight gives one whole with seven eighths left over, so the mixed form is 1 7/8. Using 875/1000 would convert only the fractional part and lose the original whole unit. This error is easy to overlook when a worksheet moves from decimals smaller than one to values larger than one. Check that the final fraction remains on the correct side of one.
Handle leading zeros and signs deliberately
The decimal 0.003125 has six decimal places, so its first fraction is 3125/1000000. Reducing by 3125 gives 1/320. The zeros after the point determine the place value even though they disappear when the numerator is read as an integer. For −2.4, keep the negative sign and form −24/10, which reduces to −12/5. A positive denominator is conventional, with the sign applied to the whole fraction. Negative twelve fifths is less than zero; accidentally dropping the sign changes the problem entirely.
Know what trailing zeros do and do not change
The written decimals 0.125 and 0.125000 represent the same exact rational number. They initially produce 125/1000 and 125000/1000000, and both reduce to 1/8. In a measurement record, trailing zeros can communicate a stated resolution or significant-figure convention, but the simplified fraction by itself does not preserve that contextual information. Keep the original measurement notation if that matters to the task. A calculator converting the numeric value cannot infer how an instrument was calibrated or whether a displayed zero was significant.
Separate finite digits from a repeating value
Entering 0.3333 describes the finite number 3333/10000. It is not exactly one third, even though it is close. A repeating decimal with threes continuing forever is a different mathematical input and needs a repeating-decimal method or the exact fraction 1/3. The local Decimal to Fraction Calculator reads the finite digits supplied in its field; it does not infer an endless repetition from a familiar-looking prefix. This distinction is important when checking equality or combining fractions, because an approximation can be useful without being identical to the intended repeating value.
Run an exact conversion and verify its scope
Type 1.875 in the local calculator and expect 15/8, together with the mixed form 1 7/8 and the original decimal. Try 0.003125 as a second independent check and expect 1/320. The converter works from the decimal text using integer arithmetic for this finite-decimal conversion, so it avoids first rounding the input to a binary floating-point approximation. It still converts only the supplied value. If a source reports 0.33 as a rounded measurement, the exact fraction 33/100 describes that written value and does not restore the unknown unrounded measurement.
Use the Decimal to Fraction Calculator
Source and scope
Related guides
Practice finite-decimal conversions with an answer key, diagnose place-value and simplification mistakes, and check a combined-fraction challenge in the local tool.
Turn repeating decimals into exact fractions by aligning and subtracting repeated digits, including mixed non-repeating prefixes and verification.
Translate between percent, decimal and fraction notation, including values below1% and above100%, and distinguish percent change from percentage-point change.