Question

Order the numbers from least to greatest.

$\mathbf{0}\mathbf{.}\mathbf{21}\mathbf{,} \mathbf{2}\mathbf{.}\mathbf{3}\mathbf{,} \frac{\mathbf{8}}{\mathbf{3}}\mathbf{,} \mathbf{-}\mathbf{0}\mathbf{.}\mathbf{1}\mathbf{,} \mathbf{-}\frac{\mathbf{1}}{\mathbf{5}}\mathbf{,} \mathbf{0}\mathbf{.}\overline{\mathbf{2}}$

Short answer

The numbers from least to greatest are $-\frac{9}{2}<-2.3<-\frac{5}{4}<-1<0.7<\frac{4}{3}$.

Step-by-step solution

Step 1. Given information

The number are $0.21,2.3,\frac{8}{3},-0.1,-\frac{1}{5},0.\overline{2}$.

Step 2. Calculation 

Write the fraction numbers as decimals.

$\begin{array}{c}0.\overline{2}=\frac{2}{9}\\ =0.22\\ 0.21,2.3,\frac{8}{3},-0.1,-\frac{1}{5},0.\overline{2}=0.21,2.3,2.66,-0.1,-0.2,0.22\end{array}$

Arrange the above numbers from least to greatest,

$-0.2<-0.1<0.21<0.22<2.3<2.66$

Thus, the numbers from least to greatest are $-\frac{1}{5}<-0.1<0.21<0.\overline{2}<2.3<\frac{8}{3}$.