Q. 5.47 - Intermediate Algebra

Question

Multiply or divide as indicated. Write answers in decimal form:

$ⓐ (-3\times {10}^5)(2\times {10}^{-8}) ⓑ \frac{8\times {10}^2}{4\times {10}^{-2}}$

Step-by-Step Solution

Answer

The decimal form of the given expression is$(-3\times {10}^5)(2\times {10}^{-8})=-0.006$

The decimal form of the given expression is $\frac{8\times {10}^2}{4\times {10}^{-2}}=20,000$

Step 1. Given Information

In the given question we have to multiply or divide and write answers in decimal form:

$ⓐ (-3\times {10}^5)(2\times {10}^{-8}) ⓑ \frac{8\times {10}^2}{4\times {10}^{-2}}$

Part (a) Step 1. The given expression is ( − 3 × 10 5 ) ( 2 × 10 − 8 )

Use the Commutative Property to rearrange the factors.

$(-3\times {10}^5)(2\times {10}^{-8})=-3·2·{10}^5·{10}^{-8}$

Multiply.

$$\begin{gathered} (-3\times {10}^5)(2\times {10}^{-8})=-6·{10}^{-8+5} \\ (-3\times {10}^5)(2\times {10}^{-8})=-6·{10}^{-3} \end{gathered}$$

Change to decimal form by moving the decimal three places left.

$$\begin{gathered} (-3\times {10}^5)(2\times {10}^{-8})=-6·\frac{1}{{10}^3} \\ (-3\times {10}^5)(2\times {10}^{-8})=-6·\frac{1}{1000} \\ (-3\times {10}^5)(2\times {10}^{-8})=-0.006 \end{gathered}$$

Part (b) Step 1. The given expression is 8 × 10 2 4 × 10 − 2

Separate the factors, rewriting as the product of two fractions.

$\frac{8\times {10}^2}{4\times {10}^{-2}}=\frac{8}{4}\times \frac{{10}^2}{{10}^{-2}}$

Divide.

$\frac{8\times {10}^2}{4\times {10}^{-2}}=2\times {10}^4$

Change to decimal form by moving the decimal four places right.

$\frac{8\times {10}^2}{4\times {10}^{-2}}=20,000$