Question

What is $33\frac{1}{3}\%$ as a fraction and decimal?

Answer 1

Convert percentages into fractions and decimals:

First, convert the mixed percentage $33\frac{1}{3}\%$ into the improper fraction percentage:

$$\begin{gathered} 33\frac{1}{3}\%=\frac{(33\times 3)+1}{3} \\ \Rightarrow =\frac{100}{3}\% \end{gathered}$$

Now convert the percentage into a fraction:

$$\begin{gathered} \therefore \frac{100}{3}\%=\frac{100}{3\times 100} \\ \Rightarrow =\frac{100}{300} \\ \Rightarrow =\frac{1}{3} \end{gathered}$$

When $1$ is divided by $3$:

$$\begin{gathered} \frac{1}{3}=0.33333333 \\ \Rightarrow =0.\overline{3} \end{gathered}$$

Hence, the required value of fraction and decimal are $\frac{1}{3}$ and $0.\overline{3}$ respectively.