Q. 171 - Intermediate Algebra

Question

In the following exercises, multiply or divide as indicated. Write your answer in decimal form.

(a) $\left(2\times {10}^2\right)\left(1\times {10}^{-4}\right)$ (b) $\frac{5\times {10}^{-2}}{1\times {10}^{-10}}$

Step-by-Step Solution

Answer

(a) Multiplied result is 0.02

(b) Divided result is 500000000

part (a) Step 1 Given information

$\left(2\times {10}^2\right)\left(1\times {10}^{-4}\right)$

part (a) Step 2

$$\begin{gathered} \left(2\times {10}^2\right)\left(1\times {10}^{-4}\right)=2\times 1\times {10}^{2-4} \\ =2\times {10}^{-2} \\ =0.02 \end{gathered}$$

part (b) Step 1 Given information

$\frac{5\times {10}^{-2}}{1\times {10}^{-10}}$

part (b) Step 2

$$\begin{gathered} \frac{5\times {10}^{-2}}{1\times {10}^{-10}}=\frac{5}{1}\times {10}^{-2+10} \\ =5\times {10}^8 \\ =500000000 \end{gathered}$$