Solve 0.9*1/3/frac{1{3}div0.9}=

$$\frac { 0.9 \times \frac { 1 } { 3 } } { \frac { 1 } { 3 } \div 0.9 } =$$

Evaluate

$$0.81$$

Solution Steps

Convert decimal number 0.9 to fraction \frac{9}{10}.

$$\frac{\frac{9}{10}\times \frac{1}{3}}{\frac{\frac{1}{3}}{0.9}}$$

Multiply \frac{9}{10} times \frac{1}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{9\times 1}{10\times 3}}{\frac{\frac{1}{3}}{0.9}}$$

Do the multiplications in the fraction \frac{9\times 1}{10\times 3}.

$$\frac{\frac{9}{30}}{\frac{\frac{1}{3}}{0.9}}$$

Reduce the fraction \frac{9}{30} to lowest terms by extracting and canceling out 3.

$$\frac{\frac{3}{10}}{\frac{\frac{1}{3}}{0.9}}$$

Express \frac{\frac{1}{3}}{0.9} as a single fraction.

$$\frac{\frac{3}{10}}{\frac{1}{3\times 0.9}}$$

Multiply 3 and 0.9 to get 2.7.

$$\frac{\frac{3}{10}}{\frac{1}{2.7}}$$

Expand \frac{1}{2.7} by multiplying both numerator and the denominator by 10.

$$\frac{\frac{3}{10}}{\frac{10}{27}}$$

Divide \frac{3}{10} by \frac{10}{27} by multiplying \frac{3}{10} by the reciprocal of \frac{10}{27}.

$$\frac{3}{10}\times \frac{27}{10}$$

Multiply \frac{3}{10} times \frac{27}{10} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3\times 27}{10\times 10}$$

Do the multiplications in the fraction \frac{3\times 27}{10\times 10}.

$$\frac{81}{100}$$

Factor

$$\frac{3 ^ {4}}{2 ^ {2} \cdot 5 ^ {2}} = 0.81$$