Question

Is 8.21 repeating a rational number?

Answer 1

We want to know if the number 8.21212121 (repeating) is a rational number.

So, the answer is yes and we will find the rational representation:

`8.212121\ldots=8+0.21212121\ldots=8+(21)/(99)=(8\cdot99+21)/(99)=(813)/(99)`

For any repeating number we can convert to a rational representation taking the repeating number and divided by the the number of 9 with equal number of digits as the repeating number.

In this case, the repeating number is 21, it has two digits so we have to divide by 99 (two digits of 9).