1. Convert pure repeating decimals to fractions

A decimal that repeats after the first decimal point is called a pure repeating decimal. How do you 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 reduced to a fraction, the numerator of which is a number represented by a repeating cycle, and the digits in the denominator are all 9. The number of 9s is the same as the number of digits in the repeating cycle.

2. Mixed recurring decimal fractions

A decimal that does not repeat from the first decimal point is called a mixed recurring decimal. How to convert a mixed recurring decimal into a fraction? Convert a mixed recurring 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 whose numerator is the difference between the number of decimal parts before the second repeating period and the number of decimal parts that do not repeat. 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.

3. Four arithmetic operations of recurring decimals

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

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

For example: 0.333.....＝3/9=1/3

0.214214214214214....=214/999

Simply put, each cycle is the numerator, and the denominator is written as many 9s as there are digits in the cycle.

0.3333......The cycle is 3 0.214.....The cycle is 214

0.52525252....The cycle number is 52, so 0.525252...＝52/99

0.35....=35/99