Elementary Mathematical Olympiad: How to Turn Recurring Decimals into Fraction

Answer 1

Recurring decimals refer to decimals with a repeating fraction, such as 06666 and 314159265358979323846. If you want to convert such decimals into scores, you can follow the following steps:

1 determines the position of the loop section, that is, the difference between the first number and the last number of the decimal part is usually the number sequence of the decimal part when the two numbers are equal. For example, 06666's repeating period is between the 6th and 7th digits of the decimal part, which means 6-7=1, so it can be expressed as 1/2.

2. The number where the loop section is located and the numbers after it are all omitted, and only the decimals are retained to obtain the fraction form. For example, 06666 could be expressed as 1/2(6/6=2/2=1+1/2).

3. If there are multiple cycles after a certain number in the decimal part, you need to first determine the last cycle and then follow the above steps. For example, the loop section of 314159265358979323846 is between the 26th and 27th digits of the decimal part, which is 26-27=-1. Therefore, you need to first determine whether the last loop section is 1 or-1 and then simplify it accordingly.

The method of converting a repeating decimal into a fraction needed to determine the last loop section according to the position of the loop section and then simplify it according to the above steps.