Question

Is
irrational or rational?

Answer 1

If we can write this expression as a fraction, then this will be rational. Otherwise, irrational.

First, let's write the repeating decimal as fraction. Excluding the 1 point to the left of the decimal.

We have:

0.234523452345...

We can write it as:

`(2345)/(9999)`

Tagging along the "1", we have:

`1(2345)/(9999)`

Then, we have square root of 4, which is "2".

If we multiply the fraction shown above by 2, we will definitely have a fraction.

That will be a rational number.