Fraction to Decimal Conversion |

### Fraction to Decimal Conversion Tables

**Important Note:** any span of numbers that is underlined signifies that those numbers are repeated. For example, 0.09 signifies 0.090909….

**Only fractions in lowest terms are listed.** For instance, to find 2/8, first simplify it to 1/4 then search for it in the table below.

fraction = decimal |
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1/1 = 1 |
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1/2 = 0.5 |
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1/3 = 0.3 |
2/3 = 0.6 | ||

1/4 = 0.25 |
3/4 = 0.75 | ||

1/5 = 0.2 |
2/5 = 0.4 | 3/5 = 0.6 | 4/5 = 0.8 |

1/6 = 0.16 |
5/6 = 0.83 | ||

1/7 = 0.142857 |
2/7 = 0.285714 | 3/7 = 0.428571 | 4/7 = 0.571428 |

5/7 = 0.714285 | 6/7 = 0.857142 | ||

1/8 = 0.125 |
3/8 = 0.375 | 5/8 = 0.625 | 7/8 = 0.875 |

1/9 = 0.1 |
2/9 = 0.2 | 4/9 = 0.4 | 5/9 = 0.5 |

7/9 = 0.7 | 8/9 = 0.8 | ||

1/10 = 0.1 |
3/10 = 0.3 | 7/10 = 0.7 | 9/10 = 0.9 |

1/11 = 0.09 |
2/11 = 0.18 | 3/11 = 0.27 | 4/11 = 0.36 |

5/11 = 0.45 | 6/11 = 0.54 | 7/11 = 0.63 | |

8/11 = 0.72 | 9/11 = 0.81 | 10/11 = 0.90 | |

1/12 = 0.083 |
5/12 = 0.416 | 7/12 = 0.583 | 11/12 = 0.916 |

1/16 = 0.0625 |
3/16 = 0.1875 | 5/16 = 0.3125 | 7/16 = 0.4375 |

11/16 = 0.6875 | 13/16 = 0.8125 | 15/16 = 0.9375 | |

1/32 = 0.03125 |
3/32 = 0.09375 | 5/32 = 0.15625 | 7/32 = 0.21875 |

9/32 = 0.28125 | 11/32 = 0.34375 | 13/32 = 0.40625 | |

15/32 = 0.46875 | 17/32 = 0.53125 | 19/32 = 0.59375 | |

21/32 = 0.65625 | 23/32 = 0.71875 | 25/32 = 0.78125 | |

27/32 = 0.84375 | 29/32 = 0.90625 | 31/32 = 0.96875 |

**Need to convert a repeating decimal to a fraction?** Follow these examples:

**Note the following pattern for repeating decimals:**

0.22222222… = 2/9

0.54545454… = 54/99

0.298298298… = 298/999

Division by 9’s causes the repeating pattern.

**Note the pattern if zeros precede the repeating decimal:**

0.022222222… = 2/90

0.00054545454… = 54/99000

0.00298298298… = 298/99900

Adding zero’s to the denominator adds zero’s before the repeating decimal.

**To convert a decimal that begins with a non-repeating part**, such as 0.21456456456456456…, to a fraction, write it as the sum of the non-repeating part and the repeating part.

0.21 + 0.00456456456456456…

Next, convert each of these decimals to fractions. The first decimal has a divisor of power ten. The second decimal (which repeats) is converted according to the pattern given above.

21/100 + 456/99900

Now add these fraction by expressing both with a common divisor

20979/99900 + 456/99900

and add.

21435/99900

Finally simplify it to lowest terms

1429/6660

and check on your calculator or with long division.

= 0.2145645645…

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