Chapter 3.1, Problem 42IP

To determine

To replace: each $\otimes$ with $<$ , >, or $=$ to make the provided sentence true.

Answer to Problem 42IP

The sign is replaced by $=$ .

Explanation of Solution

Given information:

Consider, the sentence provided with two numbers, $\text{0}\text{.}\overline{\text{54}}\otimes \frac{6}{11}$ .

Consider the numbers $\text{0}\text{.}\overline{\text{54}}$ and $\frac{6}{11}$ , the decimal form of the fraction $\frac{6}{11}$ is $\text{0}\text{.}\overline{\text{54}}$ .

As, the decimal values of $\frac{6}{11}$ and $\text{0}\text{.}\overline{\text{54}}$ are equal.

So, the sign is replaced by $=$ , and the sentence is written as $\text{0}\text{.}\overline{\text{54}}=\frac{6}{11}$ .