Chapter 3.1, Problem 49PPS

To determine

ToDetermineOrder the group of numbers $2\frac{3}{5}$ , $2.67$ , $2\frac{2}{3}$ from least to greatest.

Answer to Problem 49PPS

Ordering the given numbers from least to greatest, we have $2.6$ , $2.\overline{6}$ , $2.67$ i.e., $2\frac{3}{5}$ , $2\frac{2}{3}$ , $2.67$

Explanation of Solution

Given:

The numbers $2\frac{3}{5}$ , $2.67$ , $2\frac{2}{3}$

Concept Used:

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

Calculation:

Given the numbers $2\frac{3}{5}$ , $2.67$ , $2\frac{2}{3}$

Converting the fractions into decimals and then comparing them all

Converting $2\frac{3}{5}$ into decimals

i.e., $2\frac{3}{5}=\frac{13}{5}$

Dividing numerator with denominator, we have

i.e., $5\begin{array}{c}\hfill 2.6\\ \hfill \overline{)\begin{array}{l}13\\ \underset{\_}{10}\\ 30\\ \underset{\_}{30}\\ 0\end{array}}\end{array}$

Thus, $2\frac{3}{5}=\frac{13}{5}=2.6$

Converting $2\frac{2}{3}$ into decimals

i.e., $2\frac{2}{3}=\frac{8}{3}$

Dividing numerator with denominator, we have

i.e., $3\begin{array}{c}\hfill 2.66\\ \hfill \overline{)\begin{array}{l}8\\ \underset{\_}{\text{6 }}\\ 20\\ \underset{\_}{18}\\ \text{ 2}0\\ \underset{\_}{18}\\ \text{ 2}\end{array}}\end{array}$

Thus, $2\frac{2}{3}=\frac{8}{3}=2.66\text{. }\text{. }\text{.}$

The repeating decimal can be written as $2\frac{2}{3}=\frac{8}{3}=2.\overline{6}$

After converting the numbers $2\frac{3}{5}$ , $2.67$ , $2\frac{2}{3}$ into decimal form, we have

  $2\frac{3}{5}=\frac{13}{5}=2.6$

  $2.67=2.67$

  $2\frac{2}{3}=\frac{8}{3}=2.\overline{6}$

Ordering them from least to greatest, we have $2.6$ , $2.\overline{6}$ , $2.67$ i.e., $2\frac{3}{5}$ , $2\frac{2}{3}$ , $2.67$

Conclusion:

Ordering the given numbers from least to greatest, we have $2.6$ , $2.\overline{6}$ , $2.67$ i.e., $2\frac{3}{5}$ , $2\frac{2}{3}$ , $2.67$