Chapter 5.2, Problem 16WE

To determine

To find: Express as a decimal numeral.

Answer to Problem 16WE

  $1.45\times {10}^{-2}=0.0145$

Explanation of Solution

Given information:

  $1.45\times {10}^{-2}$

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.

  $1.45\times {10}^{-2}$

  $\begin{array}{l}\Rightarrow 1.45\times {10}^{-2}=1.45\times \frac{1}{{10}^2}\\ \Rightarrow 1.45\times {10}^{-2}=1.45\times \frac{1}{100}\\ \Rightarrow 1.45\times {10}^{-2}=\frac{1.45}{100}\\ \Rightarrow 1.45\times {10}^{-2}=0.0145\end{array}$

Therefore,

  $1.45\times {10}^{-2}=0.0145$