## Conversion stages

- Write the decimal fraction as a fraction of the digits to the right of the decimal period (numerator) and a power of 10 (denominator).
- Find the greatest common divisor (gcd) of the numerator and the denominator.
- Reduce the fraction by dividing the numerator and the denominator with the gcd.

#### Example #1

Convert 0.32 to fraction:

0.32 = 32/100

Find the greatest common divisor (gcd) of the numerator and the denominator:

gcd(32,100) = 4

Reduce the fraction by dividing the numerator and the denominator with the gcd:

0.32 = (32/4) / (100/4) = 8/25

#### Example #2

Convert 2.56 to fraction:

2.56 = 2+56/100

Find the greatest common divisor (gcd) of the numerator and the denominator:

gcd(56,100) = 4

Reduce the fraction by dividing the numerator and the denominator with the gcd:

2+56/100 = 2 + (56/4) / (100/4) = 2+14/25

#### Example #3

Convert 0.124 to fraction:

0.124 = 124/1000

Find the greatest common divisor (gcd) of the numerator and the denominator:

gcd(124,1000) = 4

Reduce the fraction by dividing the numerator and the denominator with the gcd:

0.124 = (124/4) / (1000/4) = 31/250

## How to convert repeating decimal to fraction

#### Example #1

Convert 0.333333... to fraction:

*x* = 0.333333...

10*x* = 3.333333...

10*x* - *x* = 9*x* = 3

*x* = 3/9 = 1/3

#### Example #2

Convert 0.0565656... to fraction:

*x* = 0.0565656...

100*x* = 5.6565656...

100*x* - *x* = 99*x* = 5.6

990*x* = 56

*x* = 56/990 = 28/495

## Decimal to fraction conversion table

Decimal | Fraction |
---|---|

0.001 | 1/1000 |

0.01 | 1/100 |

0.1 | 1/10 |

0.11111111 | 1/9 |

0.125 | 1/8 |

0.14285714 | 1/7 |

0.16666667 | 1/6 |

0.2 | 1/5 |

0.22222222 | 2/9 |

0.25 | 1/4 |

0.28571429 | 2/7 |

0.3 | 3/10 |

0.33333333 | 1/3 |

0.375 | 3/8 |

0.4 | 2/5 |

0.42857143 | 3/7 |

0.44444444 | 4/9 |

0.5 | 1/2 |

0.55555555 | 5/9 |

0.57142858 | 4/7 |

0.625 | 5/8 |

0.66666667 | 2/3 |

0.6 | 3/5 |

0.7 | 7/10 |

0.71428571 | 5/7 |

0.75 | 3/4 |

0.77777778 | 7/9 |

0.8 | 4/5 |

0.83333333 | 5/6 |

0.85714286 | 6/7 |

0.875 | 7/8 |

0.88888889 | 8/9 |

0.9 | 9/10 |

Decimal to fraction converter »

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