Question

Is 4.3 repeating rational or irrational

Answer 1

We have the number:

`4.\bar{3}`

We have to answer if it is rational or irrational.

In order to be rational, a number has to be able to be represented in a fraction.

In this case, we start by separating the number in the whole part and the decimal part:

`4.\bar{3}=4+0.33333\ldots`

We can express the decimal part as a fraction, because:

`(1)/(3)=0.333333\ldots`

Then, we have:

`4.\bar{3}=4+0.333\ldots=4+(1)/(3)=(4\cdot3+1)/(3)=(13)/(3)`

As we have a fractional expresion for the number, it is not an irrational number.

4.3... is a rational number.