We have the number:
[tex]4.\bar{3}[/tex]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:
[tex]4.\bar{3}=4+0.33333\ldots[/tex]We can express the decimal part as a fraction, because:
[tex]\frac{1}{3}=0.333333\ldots[/tex]Then, we have:
[tex]4.\bar{3}=4+0.333\ldots=4+\frac{1}{3}=\frac{4\cdot3+1}{3}=\frac{13}{3}[/tex]As we have a fractional expresion for the number, it is not an irrational number.
4.3... is a rational number.
