Decimal to Fraction

Write the decimal divided by 1, then multiply numerator and denominator by 10 for every number after decimal point. Simplify the fraction. Example: 0.75 = 75/100 = 3/4. For repeating decimals, use a different method or our calculator.

For 0.333... (1/3): Let x = 0.333..., multiply by 10: 10x = 3.333..., subtract: 9x = 3, so x = 3/9 = 1/3. For 0.1666... (1/6): x = 0.1666..., 10x = 1.666..., 100x = 16.666..., subtract: 90x = 15, x = 15/90 = 1/6.

A terminating decimal has a finite number of digits. Example: 0.5, 0.75, 0.125. These decimals can be written as fractions with denominators that are powers of 2 and/or 5. 0.125 = 1/8, 0.2 = 1/5.

A repeating decimal has digits that repeat infinitely. Example: 0.333... (1/3), 0.666... (2/3), 0.1666... (1/6). Repeating decimals occur when the denominator has prime factors other than 2 and 5.