This calculator can be used to convert decimal numbers to fractions and mixed numbers (or vice versa). Periodic decimal numbers can also be entered. In addition to the result, a calculation path is also provided.

## Convert decimal number to fraction

A decimal number can be converted to a fraction very easily. The number is written into the numerator, leaving out the decimal point. If there is only a 0 before the decimal point, this is also not written down. In the denominator you write a 1 followed by as many zeros as the decimal number has decimal places. If you want, you can simplify the fraction afterwards.

Examples:

3 |

10 |

125 |

100 |

5 |

4 |

25221 |

1000 |

## Convert decimal number to mixed number

If a decimal number is to be converted into a mixed number, one proceeds very similarly to the conversion into a fraction. This time, however, only the decimal places are written in the numerator and the digits before the decimal point are written before the fraction. In the denominator again a 1 is written followed by as many zeros as the decimal number has decimal places.

Examples:

25 |

100 |

1 |

4 |

221 |

1000 |

5 |

10 |

1 |

2 |

## Convert periodic decimal number to fraction or mixed number

First you have to look at whether the periodic part starts directly at the first decimal place or behind it. If it starts directly at the first decimal place, this is the easy case. If it starts at a later decimal place, a little more effort is needed.

### Periodic part starts at first decimal place:

Let us first consider the case where the period bar starts directly at the first decimal place and where there is just a 0 in front of the decimal point. Then the decimal places are written into the numerator and as many 9s are appended to the denominator as the number has decimal places below the bar.

Examples:

12 |

99 |

4 |

33 |

3 |

9 |

1 |

3 |

125 |

999 |

125 |

999 |

3 |

9 |

1 |

3 |

If you want to represent the number as a fraction rather than a mixed number, you still have to convert the mixed number to a improper fraction by converting the integer part to a fraction that has the same denominator as the fraction and then add the two fractions.

Example:

1 |

3 |

1 |

3 |

5 ∙ 3 |

3 |

1 |

3 |

15 |

3 |

1 |

3 |

16 |

3 |

### Periodic part starts after first decimal place:

Now we come to the case that the vinculum starts behind the first decimal place. In this case, the comma must be shifted to the right until it is directly in front of the digit above which the vinculum begins. This is done by multiplying the decimal number by a power of 10 (10, 100, 1000, 10000, ...). For example, if the number 1.221 is to be converted into a fraction, then multiply the number by 100 to get 122.1. This periodic decimal number is converted to a fraction as described above. At the end, you still have to divide the fraction by the number it was multiplied by at the beginning to move the decimal point.

Example:

1.221 is to be converted into a fraction.

First, multiply by 100 to shift the decimal point so that it is directly in front of the number above which the vinculum begins. This results in 122,1.

Now the 122.1 is converted to a mixed number and then to a fraction::

1 |

9 |

122 ∙ 9 |

9 |

1 |

9 |

1099 |

9 |

Now the fraction still has to be divided by 100. This is achieved by multiplying the denominator by 100:

1099 |

9∙100 |

1099 |

900 |

1099 |

900 |

1099 |

900 |

900 |

900 |

199 |

900 |

199 |

900 |

## Convert fraction or mixed number to decimal number

To convert a fraction into a decimal number, the numerator must be divided by the denominator. If a mixed number is to be converted to a decimal number, then the result of the division is added to the integer part that precedes the fraction.

Examples:

3 |

25 |

3 |

25 |