Convert a Decimal to a Fraction Exactly

Use the decimal place value as the denominator

For a terminating decimal with k digits after the decimal point, write its signed integer digits over 10^k and reduce. Thus 0.375 becomes 375/1000. Dividing numerator and denominator by 125 gives 3/8. The three decimal places require a denominator of one thousand before simplification. Using 375/100 would instead represent 3.75, ten times the intended value. A quick decimal magnitude check can detect that misplaced power of ten before the fraction is reduced.

Include the whole-number portion

For 2.125, move the decimal point three places to obtain 2125/1000. Dividing both by 125 gives 17/8, equivalent to 2 1/8. The numerator includes all digits, not just the fractional portion 125. In the local converter, entering 2.125 should return the reduced improper fraction and a mixed-number representation. Both have the same value. Choose the improper form for further fraction multiplication or division and the mixed form when a measurement convention asks for whole units plus a remainder.

Preserve the sign of the entire value

The decimal −1.20 is −120/100 = −6/5, or −1 1/5 in conventional mixed notation. It is not −1 + 1/5. Trailing zeros do not change the rational value: −1.2 and −1.200 produce the same simplified fraction. They may communicate measurement precision in a separate scientific context, but simplification does not retain that measurement metadata. Keep the original written measurement if the number of significant digits matters alongside the exact numerical fraction.

Distinguish a finite decimal from an infinite repetition

The finite input 0.333 equals 333/1000 exactly. The repeating decimal 0.333… equals 1/3, but the ellipsis changes the mathematical statement: it says the threes continue indefinitely. A finite-decimal input box does not infer that missing infinite tail. Do not type a few repeated digits and expect the converter to choose the intended repeating rational number. State a repeating block mathematically and use its algebraic conversion separately when that is the actual question.

Convert a repeating block by algebra when needed

Let x = 0.272727… with the block 27 repeating. Then 100x = 27.272727…, so subtraction gives 99x = 27 and x = 27/99 = 3/11. For 0.1666… with only the six repeating, let x be that value; 100x − 10x = 16.666… − 1.666… = 15, giving x = 15/90 = 1/6. These are manual algebra examples, not claims that the local terminating-decimal field accepts ellipses or repeating-bar notation.

Check by converting the fraction back

Dividing 3 by 8 returns 0.375, and dividing 17 by 8 returns 2.125. Such reverse checks confirm the power of ten and simplification. A reduced fraction has a terminating base-ten decimal precisely when its positive denominator has no prime factors other than two and five. For example, 3/40 terminates because 40 = 2^3×5, while 1/6 repeats because its denominator includes three. The criterion applies after reduction; 3/6 reduces to 1/2 and therefore terminates despite the unreduced denominator six.

Do not invent precision from a rounded measurement

If 0.67 was obtained by rounding 2/3 to two decimal places, converting the displayed 0.67 gives 67/100. That conversion is correct for the displayed input but cannot reconstruct the discarded information uniquely. Many underlying values round to 0.67. Use the original exact fraction when it is known, or retain the measurement's stated precision when it is not. A mathematically exact conversion of recorded digits is different from proof that the recorded digits exactly describe the measured quantity.

Treat a percent sign as another conversion step

A percentage is a number per hundred. Therefore 37.5% means 37.5/100 = 0.375 = 3/8. Entering 37.5 by itself into a decimal converter produces 75/2, which is correct for that plain number but is one hundred times the percentage value. Remove the percent notation by dividing by one hundred first, then convert the resulting decimal. The input field expects the numerical decimal value, so keep percentage interpretation outside the fraction conversion step.

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