Chapter 3.1, Problem 50PPS

To determine

ToDetermineOrder the group of numbers $-1.\overline{1}$ , $-1\frac{1}{8}$ , $-1\frac{1}{10}$ from least to greatest.

Answer to Problem 50PPS

Ordering the given numbers from least to greatest, we have $-1.125$ , $-1.\overline{1}$ , $-1.1$ i.e., $-1\frac{1}{8}$ , $-1.\overline{1}$ , $-1\frac{1}{10}$

Explanation of Solution

Given:

The numbers $-1.\overline{1}$ , $-1\frac{1}{8}$ , $-1\frac{1}{10}$

Concept Used:

A fraction can be converted into decimal form by dividing numerator of the fraction with its denominator.

Calculation:

Given the numbers $-1.\overline{1}$ , $-1\frac{1}{8}$ , $-1\frac{1}{10}$

Converting the fractions into decimals and then comparing them all

Converting $-1\frac{1}{8}$ into decimals

i.e., $-1\frac{1}{8}=-\frac{9}{8}$

Dividing numerator with denominator, we have

i.e., $8\begin{array}{c}\hfill 1.125\\ \hfill \overline{)\begin{array}{l}9\\ \underset{\_}{8}\\ 10\\ \underset{\_}{8}\\ \text{ 20}\\ \underset{\_}{16}\\ \text{ 40}\\ \underset{\_}{40}\\ \text{ 0 }\end{array}}\end{array}$

Thus, $-1\frac{1}{8}=-\frac{9}{8}=-1.125$

Converting $-1\frac{1}{10}$ into decimals

i.e., $-1\frac{1}{10}=-\frac{11}{10}$

Dividing numerator with denominator, we have

i.e., $10\begin{array}{c}\hfill 1.1\\ \hfill \overline{)\begin{array}{l}11\\ \underset{\_}{\text{10 }}\\ 10\\ \underset{\_}{\text{10 }}\\ \text{ 0}\end{array}}\end{array}$

Thus, $-1\frac{1}{10}=-\frac{11}{10}=-1.1$

After converting the numbers $-1.\overline{1}$ , $-1\frac{1}{8}$ , $-1\frac{1}{10}$ into decimal form, we have

  $-1.\overline{1}=-1.\overline{1}$

  $-1\frac{1}{8}=-1.125$

  $-1\frac{1}{10}=-1.1$

Ordering them from least to greatest, we have $-1.125$ , $-1.\overline{1}$ , $-1.1$ i.e., $-1\frac{1}{8}$ , $-1.\overline{1}$ , $-1\frac{1}{10}$

Conclusion:

Ordering the given numbers from least to greatest, we have $-1.125$ , $-1.\overline{1}$ , $-1.1$ i.e., $-1\frac{1}{8}$ , $-1.\overline{1}$ , $-1\frac{1}{10}$