Question

Order the numbers from least to greatest.

$\mathbf{0}\mathbf{.}\mathbf{3}\mathbf{,} \mathbf{0}\mathbf{.}\overline{\mathbf{3}}\mathbf{,}\mathbf{0}\mathbf{.}\overline{\mathbf{30}}\mathbf{,}\mathbf{-}\mathbf{0}\mathbf{.}\mathbf{3}\mathbf{,}\mathbf{-}\mathbf{0}\mathbf{.}\overline{\mathbf{3}}$

Short answer

The numbers from least to greatest are $\mathbf{-}\mathbf{0}\mathbf{.}\overline{\mathbf{3}}\mathbf{<}\mathbf{-}\mathbf{0}\mathbf{.}\mathbf{3}\mathbf{<}\mathbf{0}\mathbf{.}\mathbf{3}\mathbf{<}\mathbf{0}\mathbf{.}\overline{\mathbf{30}}\mathbf{<}\mathbf{0}\mathbf{.}\overline{\mathbf{3}}$.

Step-by-step solution

Step 1. Given information

The number are $0.3,0.\overline{3},0.\overline{30},-0.3,-0.\overline{3}$.

Step 2. Calculation 

Write the fraction numbers as decimals.

$\begin{array}{c}0.\overline{30}=\frac{30}{99}\\ =0.3030\end{array}$

$\begin{array}{c}0.\overline{3}=\frac{3}{9}\\ =0.3333\end{array}$

$0.3,0.\overline{3},0.\overline{30},-0.3,-0.\overline{3}=0.3,0.3333,0.3030,-0.3,-0.33$

Arrange the above numbers from least to greatest,

$-0.33<-0.3<0.3<0.30<0.33$

Thus, the numbers from least to greatest are $-0.\overline{3}<-0.3<0.3<0.\overline{30}<0.\overline{3}$.