Converts a repeating decimal entered with a decimal and a repeating number of digits into a fraction.

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.

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.

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.

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