Questions: What is the reciprocal of 0.20 and 5^2 / 3 ? A 5 and 3 / 17 B 2 and 3 / 17 C 5 and 17 / 3 D 5 and 3 / 10

Solution Steps

The problem asks for the reciprocal of two numbers: 0.20 and $5 \frac{2}{3}$. We need to find the reciprocal of each number and then match our results with the given multiple-choice options.

The reciprocal of a number $x$ is $\frac{1}{x}$. For 0.20, the reciprocal is:

$$\frac{1}{0.20} = \frac{1}{\frac{1}{5}} = 5$$

First, convert the mixed number $5 \frac{2}{3}$ to an improper fraction:

$$5 \frac{2}{3} = \frac{5 \times 3 + 2}{3} = \frac{15 + 2}{3} = \frac{17}{3}$$

The reciprocal of $\frac{17}{3}$ is:

$$\frac{1}{\frac{17}{3}} = \frac{3}{17}$$

Final Answer