Question

How can a repeating decimal be a rational number?

Answer 1

hey there,

Repeating decimals are considered rational numbers because they can be represented as a ratio of two integers.

To represent any pattern of repeating decimals, divide the section of the pattern to be repeated by 9's, in the following way:

0.2222222222... = 2/9

0.252525252525... = 25/99

0.1234567123456712345671234567... = 1234567/9999999

The number of 9's in the denominator should be the same as the number of digits in the repeated block. These rational numbers may of course be reducible, if the top is divisible by 9, or both the top and bottom are divisible by another number. But this is a starting point which will always get you what you want.