Is 2.125 rational or irrational

Step by step

The question

Question: is 2.125 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 Write it as a fraction

The last digit is in the thousandths.

So we write it over 1000.

2.125 is 2125/1000.

That makes simpler: 17/8.

So 2.125 is rational.

Its decimal stops, and it is a fraction of whole numbers.

2 Check

Let's check: 17 divided by 8 is 2.125.

We get the decimal back.

So the answer is right!

Let's look back.

First: write it as a fraction.

Last: check.