Question

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

(a) $\left(3.5\times {10}^{-4}\right)\left(1.6\times {10}^{-2}\right)$ (b)$\frac{8\times {10}^6}{4\times {10}^{-1}}$

Short answer

(a) Multiplied result is 0.000056

(b) Divided result is 20000000

Step-by-step solution

part (a) Step 1 Given information  

$\left(3.5\times {10}^{-4}\right)\left(1.6\times {10}^{-2}\right)$

part (a) Step 2 

$$\begin{gathered} \left(3.5\times {10}^{-4}\right)\left(1.6\times {10}^{-2}\right)=3.5\times 1.6\times {10}^{-4-2} \\ =5.6\times {10}^{-6} \\ =0.0000056 \end{gathered}$$

part (b) Step 1 Given information  

$\frac{8\times {10}^6}{4\times {10}^{-1}}$

part (b) Step 2 

$$\begin{gathered} \frac{8\times {10}^6}{4\times {10}^{-1}}=\frac{8}{4}\times {10}^{6+1} \\ =2\times {10}^7 \\ =20000000 \end{gathered}$$