1. purely recurring decimal 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 example below.

convert fractions to pure recurring decimals:

the decimal part of a pure recurring decimal can be converted into a fraction. the numerator of this fraction is the number represented by a recurring section, and the number in each digit of the denominator is 9. the number of 9s is the same as the number of digits in the recurring section. offer points that can be reduced.

2. mixed cycle decimal fractions

decimals that do not repeat after the first decimal point are called mixed-recurring decimals. how to convert mixed decimals into fractions? convert mixed decimal fractions.

(2) first look at the decimal part 0.353

the decimal part of a mixed cyclic decimal can be converted into a fraction. the numerator of this fraction is the difference between the number composed of the decimal part before the second cyclic section and the number composed of the non-cyclic part of 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 cyclic section, and the number of 0s is the same as the number of digits in the non-cyclic part.

3. four arithmetic operations on 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, and they are also the four arithmetic operations of fractions.

to convert a finite decimal into a fraction, simply remove the decimal point, and the denominator can be converted into tens, hundreds, millions, etc. make an appointment again.

for example: 0.333....=3/9=1/3

0.214214214214214....=214/999

to put it simply, each loop section is a numerator. if the denominator of the loop section has several digits, write how many 9s there are.

0.3333......the cycle section is 3 0.214....the cycle section is 214

0.52525252....the cycle section is 52, so 0.525252...=52/99

0.35....=35/99