Chapter 5.2, Problem 15WE

To determine

To find: Express as a decimal numeral.

Answer to Problem 15WE

  $7.2\times {10}^{-3}=0.0072$

Explanation of Solution

Given information:

  $7.2\times {10}^{-3}$

Concept:

  $\frac{a}{b}\cdot \frac{c}{d}=\frac{a\cdot c}{b\cdot d}$

Using law of exponents

  $\begin{array}{l}{a}^{-m}=\frac{1}{a^m}\\ a^m\cdot a^n=a^{m+n}\\ \frac{a^m}{a^n}=a^{m-n}\\ a^0=1\end{array}$

  ${\left(a^n\right)}^m=a^{mn}$

Where $a$ be any value.

  $7.2\times {10}^{-3}$

  $\begin{array}{l}\Rightarrow 7.2\times {10}^{-3}=7.2\times \frac{1}{{10}^3}\\ \Rightarrow 7.2\times {10}^{-3}=7.2\times \frac{1}{1000}\\ \Rightarrow 7.2\times {10}^{-3}=\frac{7.2}{1000}\\ \Rightarrow 7.2\times {10}^{-3}=0.0072\end{array}$

Therefore,

  $7.2\times {10}^{-3}=0.0072$