Is 1.010010001... rational or irrational

Step by step

The question

Question: is 1.010010001… 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

Look at the digits.

Each time the pattern gets longer.

So no block of digits repeats.

So 1.010010001… is irrational.

Its decimal never stops and never repeats.

2 Check

Let's check: it goes on for ever, and no block repeats.

So no fraction makes it.

So the answer is right!

Let's look back.

First: look at the decimal.

Last: check.