Converts repeating decimals to fractions.

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- Decimal and Fraction Calculator
- Repeating Decimal to Fraction

## Repeating Decimal to Fraction

## About converting repeating decimals to fractions

Enter a decimal number and the number of repeating digits, and click the "Convert to fraction" button to convert the entered repeating decimal number into a fraction and display it.

You can enter up to 12 decimal digits. Also, please make sure to enter a number for the number of repeating digits that is greater than the number of digits after the decimal point in the entered decimal.

The converted fraction will be displayed as an improper fraction and a mixed number.

It also includes a calculation for converting a repeating decimal to a fraction.

## About repeating decimals

A repeating decimal is a decimal number in which the same sequence of digits is repeated infinitely starting from a certain digit after the decimal point.

For example, when 13 is converted to a decimal it becomes 0.333333.... and continues forever.

Such repeating decimals are represented by placing a line over the repeating part, like this: 0.3.

When 037 is repeated, such as 0.037037037..., the entire repeated part is underlined and expressed as 0.037.

## How to convert repeating decimals to fractions

- Convert repeating decimals to fractions
- 1. First, create an equation with X as a repeating decimal.
- 2. Create another equation by multiplying both sides by a power of 10 equal to the number of repeated digits in the repeating decimal.
- 3. By subtracting the two equations, we get the equation for X with the repeated parts eliminated.
- 4. By solving this equation for X, we can find X.
- 5. If possible, simplify the fraction.

### Calculation example

Example: Convert 1.45 to a fraction

Method of calculation

Let the decimal be X.

X = 1.45

To shift the number of repeated digits, multiply both sides by the power of 10 for the number of digits.

100X = 145.45

Subtract both sides.

100X | = | 145 | . | 45... | |

- | X | = | 1 | . | 45... |

99X | = | 144 |

Solve this for X.

99X = 144

X = 14499

If it is possible to simplify, simplify by dividing the numerator and denominator by 9 (the greatest common divisor of the numerator and denominator).

144 ÷ 999 ÷ 9 = 1611

Convert the improper fraction into a mixed number.

1611 = 1511

Therefore

1.45 = 1511