Chapter 3.1, Problem 48PPS

To determine

ToDetermineOrder the group of numbers $-0.29$ , $-\frac{3}{11}$ , $-\frac{2}{7}$ from least to greatest.

Answer to Problem 48PPS

Ordering the given numbers from least to greatest, we have $-0.29$ , $-0.\overline{285714}$ , $-0.\overline{27}$ i.e., $-0.29$ , $-\frac{2}{7}$ , $-\frac{3}{11}$

Explanation of Solution

Given:

The numbers $-0.29$ , $-\frac{3}{11}$ , $-\frac{2}{7}$

Concept Used:

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

Calculation:

Given the numbers $-0.29$ , $-\frac{3}{11}$ , $-\frac{2}{7}$

Converting the fractions into decimals and then comparing them all

Converting $-\frac{3}{11}$ into decimals

Dividing numerator with denominator, we have

i.e., $11\begin{array}{c}\hfill 0.2727\\ \hfill \overline{)\begin{array}{l}3\\ \underset{\_}{0}\\ 30\\ \underset{\_}{22}\\ \text{ 8}0\\ \underset{\_}{\text{77}}\\ \text{ 30}\\ \underset{\_}{22}\\ \text{ 8}0\\ \underset{\_}{\text{77}}\\ \text{ 3 }\end{array}}\end{array}$

Thus, $-\frac{3}{11}=-0.2727\text{. }\text{. }\text{.}$

The repeating decimal can be written as $-\frac{3}{11}=-0.\overline{27}$

Converting $-\frac{2}{7}$ into decimals

Dividing numerator with denominator, we have

i.e., $7\begin{array}{c}\hfill 0.2857142\\ \hfill \overline{)\begin{array}{l}2\\ \underset{\_}{0}\\ 20\\ \underset{\_}{14}\\ \text{ 6}0\\ \underset{\_}{56}\\ \text{ 40}\\ \underset{\_}{35}\\ \text{ 5}0\\ \underset{\_}{49}\\ \text{ 10}\\ \underset{\_}{7}\\ \text{ 3}0\\ \underset{\_}{28}\\ \text{ 20}\\ \underset{\_}{14}\\ \text{ 6}\end{array}}\end{array}$

Thus, $-\frac{2}{7}=-0.2857142\text{. }\text{. }\text{.}$

The repeating decimal can be written as $-\frac{2}{7}=-0.\overline{285714}$

After converting the numbers $-0.29$ , $-\frac{3}{11}$ , $-\frac{2}{7}$ into decimal form, we have

  $-0.29=-0.29$

  $-\frac{3}{11}=-0.\overline{27}$

  $-\frac{2}{7}=-0.\overline{285714}$

Ordering them from least to greatest, we have $-0.29$ , $-0.\overline{285714}$ , $-0.\overline{27}$ i.e., $-0.29$ , $-\frac{2}{7}$ , $-\frac{3}{11}$

Conclusion:

Ordering the given numbers from least to greatest, we have $-0.29$ , $-0.\overline{285714}$ , $-0.\overline{27}$ i.e., $-0.29$ , $-\frac{2}{7}$ , $-\frac{3}{11}$