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