Chapter 11.2, Problem 38WE

To determine

To find: The product of the numbers after converting into fractional form

Answer to Problem 38WE

The product of the two numbers is $\frac{1}{4}$

Explanation of Solution

Given information:

The given rational number is:

  $\begin{array}{l}{n}_1=\frac{9}{20}\\ n_2=0.\overline{5}\end{array}$

Converting the decimal expansion of a number in fractional form:

  $\begin{array}{c}{n}_2=0.\overline{5}\\ =\frac{5}{9}\end{array}$

Calculating the product of two numbers:

  $\begin{array}{l}N=n_1\times n_2\\ N=\frac{9}{20}\times \frac{5}{9}\\ N=\frac{1}{4}\end{array}$

Thus, the product of the two numbers is $\frac{1}{4}$