Question

How do you change $0.8$ into a fraction?

Answer 1

To convert the decimal number in fraction:

Re-write the given number as:

$0.8=\frac{0.8}{1}$

Multiply by $10$ in numerator and denominator:

$\begin{array}{rcl}0.8& =& 0.8\times \frac{10}{10}\\ & \Rightarrow & 0.8=\frac{0.8\times 10}{10}\left[\text{Simplifying}\right]\\ & \Rightarrow & 0.8=\frac{8}{10}\\ & \Rightarrow & 0.8=\frac{2\times 2\times 2}{2\times 5}\left[\text{Break into prime factor}\right]\\ \therefore 0.8& =& \frac{4}{5}\end{array}$

Hence, the fraction of $\mathbf{0}\mathbf{.}\mathbf{8}$ is $\frac{\mathbf{4}}{\mathbf{5}}$.