Chapter 3.1, Problem 46IP

To determine

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

Answer to Problem 46IP

The sign is replaced by $<$ .

Explanation of Solution

Given information:

Consider, the sentence provided with two numbers, $-5\frac{1}{3}\otimes -5\frac{3}{10}$ .

Consider the numbers $-5\frac{1}{3}$ and $-5\frac{3}{10}$ , both the number is in improper fraction. First it is needed to be converted in to proper fraction and then the decimal value of it is to be found.

Proper fraction of $-5\frac{1}{3}$ is $-\frac{16}{3}$ and $-5\frac{3}{10}$ is $-\frac{53}{10}$ .

Decimal value of $-5\frac{1}{3}$ is $-5.\overline{3}$ and that of $-5\frac{3}{10}$ is $-5.3$

As, the decimal values of $-5\frac{1}{3}$ is smaller than $-5\frac{3}{10}$ ,

So, the sign is replaced by $<$ , and the sentence is written as $-5\frac{1}{3}<-5\frac{3}{10}$ .