Question

Represent the following mixed infinite decimal periodic fractions as common fractions:
$\frac{(0.6{)}^0-(0.1{)}^{-1}}{{\left(\frac{3}{2^3}\right)}^{-1}\cdot {\left(\frac{3}{2}\right)}^3+{(-\frac{1}{3})}^{-1}}$

Answer 1

$\frac{(0.6{)}^0-(0.1{)}^{-1}}{{\left(\frac{3}{2^3}\right)}^{-1}\cdot {\left(\frac{3}{2}\right)}^3+{(-\frac{1}{3})}^{-1}}$

$=\frac{1-10}{\frac{8}{3}.\frac{27}{8}-3}$ ..... $(x^0=1)$

$=\frac{-9}{9-3}$

$=\frac{-9}{6}$

$=\frac{-3}{2}$