Chapter 0.4, Problem 9E

To determine

To calculate: The order of set of rational numbers $0.11,-\frac{1}{9},-0.5,\frac{1}{10}$ from least to greatest.

Answer to Problem 9E

The correct order of rational numbers from least to greatest is $-0.5<-\frac{1}{9}<0.11<\frac{1}{10}$ .

Explanation of Solution

Given information:

The set of rational numbers $0.11,-\frac{1}{9},-0.5,\frac{1}{10}$ .

Formula used:

Rational numbers are of the form $\frac{p}{q}$ where p and q are integers and $\text{q}\ne \text{0}$ .

Calculation:

Consider the provided statement “ The set of rational numbers $0.11,-\frac{1}{9},-0.5,\frac{1}{10}$ .”

Convert $-\frac{1}{9}$ and $\frac{1}{10}$ into decimal notation and then compare the set of rational numbers.

Decimal notation for $-\frac{1}{9}$ is $-0.\overline{1}$ .

Decimal notation for $\frac{1}{10}$ is $0.1$ .

Thus, the set of rational number $0.11,-\frac{1}{9},-0.5,\frac{1}{10}$ becomes $0.11,-0.\overline{1},-0.5,0.1$ .

Now, arrange this set of rational numbers from least to greatest as,

  $\begin{array}{l}-0.5<-0.\overline{1}<0.11<0.1\\ -0.5<-\frac{1}{9}<0.11<\frac{1}{10}\end{array}$

Hence, the correct order of rational numbers from least to greatest is $-0.5<-\frac{1}{9}<0.11<\frac{1}{10}$ .