Mathematics CalcyZone Calculator

Decimal to Fraction Calculator

Convert terminating or repeating decimals into exact simplified fractions.

Decimal Number

Calculation Solution

Fraction: 100/1

Exact Fraction: 100 / 1

Mathematical Formula

Fraction = (Decimal * 10^n) / 10^n simplified by GCD

Overview & Explanation

Converting a decimal to a fraction expresses a decimal number as a ratio of two integers.

How It Works

Count decimal places n.
Multiply decimal by 10^n to form numerator.
Set 10^n as denominator and simplify by GCD.

Practical Applications

Converting metric measurements to imperial fractional inches.

Fractions for measurements

Imperial measurements often use halves, quarters, eighths and sixteenths, so it helps to round a decimal to the nearest of these. Multiply the decimal part by 16 and round: 0.3 × 16 = 4.8, which rounds to 5, giving 5/16 inch (0.3125). The error is 0.0125 inch, about a third of a millimetre, which is fine for woodwork but not for machining.

Terminating decimals

Write the decimal over the matching power of ten, then simplify. 0.375 has three decimal places, so it is 375/1000; dividing both by their GCD, 125, gives 3/8. Likewise 0.6 = 6/10 = 3/5 and 2.25 = 225/100 = 9/4, or 2 1/4 as a mixed number.

Repeating decimals

Repeating decimals are also exact fractions. For 0.272727…, let x = 0.2727…; multiplying by 100 shifts one repeating block: 100x = 27.2727…. Subtracting, 99x = 27, so x = 27/99 = 3/11.

When only part repeats, as in 0.1666…, multiply to move the non-repeating part first: 10x = 1.666… and 100x = 16.666…, so 90x = 15 and x = 15/90 = 1/6. Common ones worth remembering: 0.333… = 1/3, 0.142857… = 1/7, 0.0909… = 1/11.

Why convert

Fractions are exact while decimals are often rounded. Measurements in inches, recipe quantities and probabilities are frequently easier to read as fractions: 0.625 inch is 5/8 inch. A rounded decimal such as 0.33 converts to 33/100, not 1/3, so enter as many digits as you have to get the intended fraction.