Is 0.666... rational or irrational

Step by step

The question

Question: is 0.666… rational or irrational?

Rational means: it can be written as a fraction, with whole numbers on top and at the bottom.

Then its decimal stops, or repeats for ever.

Irrational means: no fraction works.

Its decimal never stops and never repeats.

1 Look at the decimal

The digit 6 repeats for ever.

A decimal that repeats is rational.

Careful!

It goes on for ever, but it repeats.

Irrational decimals never repeat.

2 Write it as a fraction

A repeating block of 1 digit goes over 9.

So 0.666 repeating is 6/9, which makes simpler: 2/3.

So 0.666… is rational.

It is a fraction of whole numbers.

3 Check

Let's check: 2 divided by 3.

We get 0.666666, and so on.

The same decimal.

So the answer is right!

Let's look back.

First: look at the decimal.

Then: write it as a fraction.

Last: check.