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Question

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

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Solution

## Step 1. Convert percentages into fractions.The given mixed fraction percentage is converted into an improper fraction as follows:$16\frac{2}{3}%=\frac{\left(16×3\right)+2}{3}\phantom{\rule{0ex}{0ex}}⇒=\frac{48+2}{3}\phantom{\rule{0ex}{0ex}}⇒=\frac{50}{3}%$To convert percentages into fractions, divide by$100$.$\therefore \frac{50}{3}%=\frac{50}{3}÷100\phantom{\rule{0ex}{0ex}}⇒=\frac{50}{3}×\frac{1}{100}\phantom{\rule{0ex}{0ex}}⇒=\frac{1}{6}$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,$\therefore \frac{1}{6}=0.166666666\phantom{\rule{0ex}{0ex}}⇒=0.1\overline{6}$Hence, the required fraction and decimal number are $\frac{1}{6}$ and $0.1\overline{6}$ respectively.

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