Chapter 5.3, Problem 23WE

To determine

To Find: Blank space that makes given statement True.

Answer to Problem 23WE

  ${\left(0.005\right)}^3>2\times {10}^{-8}$

Explanation of Solution

Given information:

  ${\left(0.005\right)}^3\underset{\_}{?}\underset{\_}{}2\times {10}^{-8}$

  ${\left(0.005\right)}^3\underset{\_}{?}\underset{\_}{}2\times {10}^{-8}$

  $\begin{array}{l}{\left(0.005\right)}^3={\left(5\times {10}^{-3}\right)}^3\\ \Rightarrow {\left(0.005\right)}^3=5^3\times {\left({10}^{-3}\right)}^3\\ \Rightarrow {\left(0.005\right)}^3=125\times {10}^{-3\times 3}\\ \Rightarrow {\left(0.005\right)}^3=125\times {10}^{-9}\\ \Rightarrow {\left(0.005\right)}^3=125\times {10}^{-1}\times {10}^{-8}\\ \Rightarrow {\left(0.005\right)}^3=125\times \frac{1}{10}\times {10}^{-8}\\ \Rightarrow {\left(0.005\right)}^3=12.5\times {10}^{-8}\end{array}$

Therefore

Both the number has ${10}^{-8}$ common so we need to compare remaining part.

Among $12.5$ and $2$

We can say $12.5$ is greater than $2$

Therefore,

  ${\left(0.005\right)}^3>2\times {10}^{-8}$