Illustrate how to convert a mixed loop decimals into a fraction! thanks

Answer 1

Mixed repeating decimals referred to decimals with a repeating structure. For example, 1/314159 could be written as 1/3(where 3 is a loop) or 1/314159(where 14159 is a loop).

If you wanted to convert the mixed loop decimals into a fraction, you needed to find the loop section where the decimal loop part was located and then divide the loop section into several parts and express it as a fraction.

For example, 1/314159 could be written as a fraction:

1/3 = 3/3 = 1
1/314159 = 3/314159 = 114159

Here, the fraction 3 and the 14159 were divided into three parts, which were represented by the fraction 1 and 114159 respectively.

Continuing example:

1/520303 can be written as a fraction:

1/5 = 2/5 = 040203
1/520303 = 2/520303 = 040203

Here, the fraction 5 and the 20303 were divided into five parts, which were represented by the scores 040203 and 20303 respectively.

By analogy, one could find the loop section where the loop part was located and then divide it into several parts and express it with scores.