Q. 5.48 - Intermediate Algebra

Question

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

$ⓐ (-3\times {10}^{-2})(3\times {10}^{-1}) ⓑ \frac{8\times {10}^4}{2\times {10}^{-1}}$

Step-by-Step Solution

Answer

The decimal form of the given expression is$(-3\times {10}^{-2})(3\times {10}^{-1})=-0.009$

The decimal form of the given expression is $\frac{8\times {10}^4}{2\times {10}^{-1}}=4,00,000$

Step 1. Given Information

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

$ⓐ (-3\times {10}^{-2})(3\times {10}^{-1}) ⓑ \frac{8\times {10}^4}{2\times {10}^{-1}}$

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

Use the Commutative Property to rearrange the factors.

$(-3\times {10}^{-2})(3\times {10}^{-1})=-3·3·{10}^{-2}·{10}^{-1}$

Multiply.

$$\begin{gathered} (-3\times {10}^{-2})(3\times {10}^{-1})=-9·{10}^{-2-1} \\ (-3\times {10}^{-2})(3\times {10}^{-1})=-9·{10}^{-3} \end{gathered}$$

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

$$\begin{gathered} (-3\times {10}^{-2})(3\times {10}^{-1})=-9·\frac{1}{{10}^3} \\ (-3\times {10}^{-2})(3\times {10}^{-1})=-9·\frac{1}{1000} \\ (-3\times {10}^{-2})(3\times {10}^{-1})=-0.009 \end{gathered}$$

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

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

$\frac{8\times {10}^4}{2\times {10}^{-1}}=\frac{8}{2}\times \frac{{10}^4}{{10}^{-1}}$

Divide.

$$\begin{gathered} \frac{8\times {10}^4}{2\times {10}^{-1}}=4\times {10}^{4+1} \\ \frac{8\times {10}^4}{2\times {10}^{-1}}=4\times {10}^5 \end{gathered}$$

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

$\frac{8\times {10}^4}{2\times {10}^{-1}}=4,00,000$