Chapter 3.1, Problem 35IP

To determine

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

Answer to Problem 35IP

The sign is replaced by $<$ .

Explanation of Solution

Given information:

Consider, the sentence provided with two numbers, $-\frac{1}{8}\otimes -\frac{1}{10}$ .

Consider the numbers $-\frac{1}{8}$ and $-\frac{1}{10}$ , the decimal form of the fraction $-\frac{1}{8}$ and $-\frac{1}{10}$ is $-0.125$ and $-0.1$ consecutively.

As, the decimal values of $-\frac{1}{8}$ is smaller than $-\frac{1}{10}$ .

So, the sign is replaced by $<$ , and the sentence is written as $-\frac{1}{8}<-\frac{1}{10}$ .