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4 votes
Is
1.2345 \: repeating \: * √(4)irrational or rational?

User Athulpraj
by
7.5k points

1 Answer

1 vote

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.

User Andrew Hoffman
by
6.6k points
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