Chapter 5.2, Problem 13WE

To determine

To find: Express as a decimal numeral.

Answer to Problem 13WE

  $596\times {10}^{-2}=5.96$

Explanation of Solution

Given information:

  $596\times {10}^{-2}$

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.

  $596\times {10}^{-2}$

  $\begin{array}{l}\Rightarrow 596\times {10}^{-2}=596\times \frac{1}{{10}^2}\\ \Rightarrow 596\times {10}^{-2}=596\times \frac{1}{100}\\ \Rightarrow 596\times {10}^{-2}=\frac{596}{100}\\ \Rightarrow 596\times {10}^{-2}=5.96\end{array}$

Therefore,

  $596\times {10}^{-2}=5.96$