Chapter 3.1, Problem 36PPS

To determine

To replace $•$ in the sentence $0.\overline{6}•\frac{5}{9}$ with $<,>,\text{or }=$ to make a true sentence.

Answer to Problem 36PPS

  $0.\overline{6}>\frac{5}{9}$

Explanation of Solution

Given:

The sentence, $0.\overline{6}•\frac{5}{9}$ .

Concept Used:

To convert a fraction into an equivalent decimal, use long division method and divide the numerator by the denominator.

Calculation:

In order to checkwhether the fraction on the left of $•$ is less than, greater than or equal to the number on the right of $•$ , first convert the fraction into equivalent decimals and then compare the numbers.

So, to convert the fraction into decimal, divide the numerator by the denominator using long division as shown below,

  $9\begin{array}{c}\hfill 0.55\\ \hfill \overline{)\begin{array}{l}5.00\\ \underset{\_}{0}\\ 50\\ \underset{\_}{45}\\ 50\\ \underset{\_}{45}\\ 5\end{array}}\end{array}$

So, in decimal form the given sentence can be written as $0.\overline{6}•0.\overline{5}$ .

Observe that the decimal number to the left of the symbol $•$ is greater than the decimal number to the right. So, replace the symbol by $>$ sign.

Thus, the true sentence is $0.\overline{6}>\frac{5}{9}$ .