Question

What is $16\frac{2}{3}\%$ as a fraction and decimal?

Answer 1

Step 1. Convert percentages into fractions.

The given mixed fraction percentage is converted into an improper fraction as follows:

$$\begin{gathered} 16\frac{2}{3}\%=\frac{(16\times 3)+2}{3} \\ \Rightarrow =\frac{48+2}{3} \\ \Rightarrow =\frac{50}{3}\% \end{gathered}$$

To convert percentages into fractions, divide by$100$.

$$\begin{gathered} \therefore \frac{50}{3}\%=\frac{50}{3}÷100 \\ \Rightarrow =\frac{50}{3}\times \frac{1}{100} \\ \Rightarrow =\frac{1}{6} \end{gathered}$$

Step 2. Convert a fraction into a decimal number.

To convert fractions into decimals, divide numerators by denominators by using the long division method.

When $1$ divided by$6$.

found that,

$$\begin{gathered} \therefore \frac{1}{6}=0.166666666 \\ \Rightarrow =0.1\overline{6} \end{gathered}$$

Hence, the required fraction and decimal number are $\frac{1}{6}$ and $0.1\overline{6}$ respectively.