Repeating decimal to fraction calculator

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1. Convert pure repeating decimals to fractions

A decimal that repeats after the first decimal point is called a pure repeating decimal. How to convert it into a fraction? See the following example.

Convert pure repeating decimals to fractions:

The decimal part of a pure repeating decimal can be converted into a fraction. The numerator of this fraction is a number represented by a repeating cycle, and the numbers in each position of the denominator are all 9. The number of 9s is the same as the number of digits in the repeating cycle. Reduce the fractions that can be reduced.

2. Convert mixed repeating decimals to fractions

A decimal that does not repeat after the first decimal point is called a mixed repeating decimal. How to convert a mixed repeating decimal into a fraction? Convert a mixed repeating decimal into a fraction.

(2) First look at the decimal part 0.353

The decimal part of a mixed repeating decimal can be converted into a fraction. The numerator of this fraction is the difference between the number of decimal parts before the second repeating period and the number of non-repeating parts in the decimal part. The first few digits of the denominator are 9, and the last few digits are 0. The number of 9s is the same as the number of digits in the repeating period, and the number of 0s is the same as the number of digits in the non-repeating part.

III. Four arithmetic operations of repeating decimals

After the repeating decimal is converted into a fraction, the four arithmetic operations of the repeating decimal can be performed according to the four arithmetic operations of fractions. In this sense, the four arithmetic operations of repeating decimals are the same as the four arithmetic operations of finite decimals, and are also the four arithmetic operations of fractions.

To convert a finite decimal into a fraction, simply remove the decimal point, and the denominator will be converted to tens, hundreds, thousands, etc. Then reduce it.

For example: 0.333.....＝3/9=1/3

0.214214214214214....=214/999

Simply put, each recurring section is the numerator, and the denominator is written as many 9s as the number of digits in the recurring section

0.3333......The recurring section is 3 0.214.....The recurring section is 214

0.52525252....The recurring section is 52, so 0.525252...＝52/99

0.35....=35/99