Give examples to illustrate the reciprocal method of fractions and decimals.

Fractions after decimalization are unchanged before the decimal point, multiplied by the n power of 10 after the decimal point, and the denominator is the n power of 10, and then reduced, for example, 1.5 is unchanged at 1. Multiply 0.5 by 10 to get 5, and the denominator is 10.

Another example is 2. 124, which means that 2 is unchanged. 0. 124 times 1000 is 124, and the denominator is 1000, which is 2 plus 250 of 3 1. Secondly, we should remember some constants such as 0.25= 1/4, 0. 125= 1/8, 0.5= 1/2, 0.2= 1/5, 0.33 … 3 =/.

Fractional decimal

1, denominator shift numerator method. Refers to the method of removing the denominator of a fraction and moving the decimal point of a molecule to the left by several digits. ?

For example, when 7/ 100 is converted into decimal, the denominator 100 is removed first, and then the decimal point of the numerator 7 is shifted to the left by two places to get 0. 07, so =0.07.

2. Relationship method. Refers to a method of converting fractions into decimals according to the relationship between fractions and decimals. For example, if 37/ 100 is converted into a decimal, we can know that the rewritten decimal is two decimal places, so it is =0.37.

When a fraction is rewritten as a decimal, there are not enough digits in the decimal part, so zero should be filled. For example, 7/ 1000 should be 0. 007.

3. Reading and writing. Refers to the method of rewriting according to the pronunciation of decimals. For example, when 9/ 10 is rewritten as a decimal, 9/ 10 can be read as nine tenths and written as a decimal 0.9.

Extended data

Fractions and decimals can be divided into three situations:

1, decimal to finite decimal. The necessary and sufficient condition for the simplest fractional reduction to a finite decimal is that the prime factors of the denominator are only 2 and 5.

2. Fractions are converted into pure cyclic decimals. The necessary and sufficient condition for the simplest fraction to be converted into a pure cyclic decimal is that there are no 2 and 5 in the prime factor of the denominator, and the number of digits in the cyclic segment is equal to the number of 9 in the minimum number of 99…9 that can be divisible by the denominator of the simplest fraction.

3. Divide the score into mixed cycle decimals. A necessary and sufficient condition for simplest fraction to be converted into a mixed cyclic decimal is that the denominator contains both prime factors 2 or 5 and prime factors other than prime factors 2 and 5. In the converted mixed cyclic decimal, the number of acyclic digits is equal to the greater of the exponent of factor 2 or factor 5 in the denominator; The number of digits in the loop segment is equal to 9 in the form of 99…9, which can be divisible by factors different from 2 and 5 in the denominator.

Baidu Encyclopedia-Fractional Decimal

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