What are the different methods to detect a repeating decimal?

There are several methods to detect a repeating decimal. One common method is to look for a pattern in the digits after the decimal point. If there is a repetitious sequence, it indicates a repeating decimal. For example, in the decimal representation of 1/3, the digit '3' repeats indefinitely after the decimal point. Another method is to use long division to divide the numerator by the denominator. If the division process results in a repeating pattern of remainders, it signifies a repeating decimal. Additionally, one can convert a repeating decimal into a fraction using algebraic techniques. This involves assigning variables to the repeating digits, forming an equation, and solving for the value of the repeating decimal. These different methods help identify and understand the nature of repeating decimals.

This mind map was published on 5 December 2023 and has been viewed 69 times.