# Decimal to Fraction Calculator

Convert a decimal value to a fraction using our calculator by entering a decimal value below. The calculator will find the reduced fraction and will show all the work so you can see how to do it. Also see our fraction to decimal calculator to see how to convert a fraction to a decimal.

## Solution:

## How to Convert a Decimal to a Fraction

Decimal and fractional numbers both represent a number that is not an even integer, or a number that is not a whole number. Every decimal number can be converted to a fraction in just three easy steps.

Note that the process to convert a repeating decimal are different.

### Step One: Create the Starting Fraction

The first step in transforming a decimal into a fraction is to create a starting fraction by making the decimal the numerator and putting that over 1 as the denominator.

**For example,** to convert .75 to a fraction, start by making .75 a fraction with .75 as the numerator and 1 as the denominator.

.75 = .751

### Step Two: Multiply by Ten to Eliminate the Decimal Place

The next step is to multiply the numerator and the denominator by 10 to get rid of the decimal place. Continue multiplying both by 10 until the numerator is an integer value, or whole number.

Continuing the example from above, let’s convert .751 to 75100

.751 = (.75 × 10)(1 × 10) = 7.510

7.510 = (7.5 × 10)(10 × 10) = 75100

### Step Three: Reduce the Fraction

The final step in converting a decimal to a fraction is to reduce or simplify the fraction. To reduce, find the greatest common factor for the numerator and denominator. Then, divide both the numerator and the denominator by the greatest common factor.

To complete the example above, we know that the greatest common factor of 75 and 100 is 25. So, let’s divide the numerator and denominator by 25 to solve the reduced fraction.

75100 = (75 ÷ 25)(100 ÷ 25)

75100 = 34

Here’s a tip: use our fraction reduction calculator to easily reduce your fraction.

For negative numbers, just remove the negative symbol from the starting decimal, then follow the steps above. After the number has been converted to fraction form, add the negative sign back.

## How to Convert a Repeating Decimal to a Fraction

Repeating decimal numbers require a slightly different process to convert to a fraction. A repeating decimal is a decimal number that continues infinitely, such as 1.1787878. These numbers are usually expressed in a rounded form, such as .788, or with an over-bar like this: 1.178.

### Step One: Create an Equation

The first step in transforming a repeating decimal is to create an algebraic equation to represent the decimal.

**For example,** let’s convert the decimal 1.178 into a fraction. Start by creating an equation to assign the expression 1.1787878 to x.

x = 1.1787878

### Step Two: Multiply by 10 Until the Repeating Decimal is on the Left

The second step is to continue multiplying both sides of the equation by 10 until the repeating number is on the left side of the decimal point. If there are multiple repeating numbers that repeat in a pattern then multiply by 10 until the repeating pattern is on the left side of the decimal point.

Continuing the example above, let’s multiply both sides of the equation by 10 until the repeating “78” part of the decimal is on the left side of the decimal point.

x = 1.1787878

10 × x = 10 × 1.1787878

10x = 11.787878

10 × 10x = 10 × 11.787878

100x = 117.87878

10 × 100x = 10 × 117.87878

1000x = 1178.78

### Step Three: Multiply by 10 Until the Repeating Decimal is on the Right

The third step is to create a new equation for x and multiply until the repeating decimal portion is to the right of the decimal point

Building on our example, multiply both sides of the equation by 10 until the repeating “78” part of the decimal is on the right side of the decimal point.

x = 1.1787878

10 × x = 10 × 1.1787878

10x = 11.78

### Step Four: Combine the Equations

The next step in the process is to combine the equations and put both x variables on the left and both of the decimal values on the right.

Let’s combine the equations and solve.

1000x – 10x = 1178.78 – 11.788

### Step Five: Solve

Finally, solve for x to convert the decimal value to a fraction.

Let’s combine the equations and solve.

1000x – 10x = 1178.78 – 11.78

990x = 1167

990x990 = 1167990

x = 1167990

## Decimal Equivalents for Common Fractions

An alternate method to convert a decimal to a fraction value is to use a conversion table such as this one. See the fraction equivalents for some common decimal values below. Use this table for convenience to see the corresponding fraction for a decimal number.

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

0.0625 | 1/16 |

0.08333 | 1/12 |

0.1 | 1/10 |

0.111 | 1/9 |

0.125 | 1/8 |

0.1666 | 1/6 |

0.2 | 1/5 |

0.222 | 2/9 |

0.25 | 1/4 |

0.333 | 1/3 |

0.375 | 3/8 |

0.4 | 2/5 |

0.444 | 4/9 |

0.5 | 1/2 |

0.555 | 5/9 |

0.6 | 3/5 |

0.625 | 5/8 |

0.666 | 2/3 |

0.75 | 3/4 |

0.777 | 7/9 |

0.8 | 4/5 |

0.8333 | 5/6 |

0.875 | 7/8 |

0.888 | 8/9 |

See more fraction decimal equivalents.