# Determine whether the number 0.121212… is rational or irrational. What is its fractional equivalent?

##### 2 Answers

#### Explanation:

we can show

Its fractional equivalent is:

We have to write the repeated number

The answer is

Rational.

#### Explanation:

We can find a fraction for the decimal this way:

First let's take the original decimal:

and then multiply it by 100:

and now subtract the two:

So up to this point what I've said is that when there is 1 of the decimal, it's

We can then reduce this:

Now that we have a fraction, let's talk about what it means for a number to be rational and what it means for it to be irrational.

A rational number, quite simply, is one that can be expressed using a fraction of integers. For example,

An irrational number is one that cannot be expressed as a fraction of integers.