Question

The decimal representation of the rational number $\frac{8}{27}$ is ___ .

Answer 1

Given rational number is $\frac{\mathbf{8}}{\mathbf{27}}$.

Dividing the numerator by denominator,

$270·29628054260243170162805426$

We can notice that, quotient decimal expression $296$ will keep on repeating, hence the given rational number is a repeating decimal number, also known as the recurring decimal number.

$\mathrm{Therefore},\frac{8}{27}=0.\overline{296}$

Final Answer :

Hence, the decimal representation of the given rational number is $0·\overline{296}$.