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Mathematics » Introducing Polynomials » Integer Exponents and Scientific Notation

# Multiplying and Dividing Using Scientific Notation

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## Multiplying and Dividing Using Scientific Notation

We use the Properties of Exponents to multiply and divide numbers in scientific notation.

## Example

Multiply. Write answers in decimal form: $$\left(4\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{5}\right)\left(2\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{-7}\right).$$

### Solution

 $$\left(4\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{5}\right)\left(2\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{-7}\right)$$ Use the Commutative Property to rearrange the factors. $$4·2·{10}^{5}·{10}^{-7}$$ Multiply 4 by 2 and use the Product Property to multiply $${10}^{5}$$ by $${10}^{-7}$$. $$8\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{-2}$$ Change to decimal form by moving the decimal two places left. $$0.08$$

## Example

Divide. Write answers in decimal form: $$\frac{9\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{3}}{3\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{-2}}.$$

### Solution

 $$\frac{9\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{3}}{3\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{-2}}$$ Separate the factors. $$\frac{9}{3}\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}\frac{{10}^{3}}{{10}^{-2}}$$ Divide 9 by 3 and use the Quotient Property to divide $${10}^{3}$$ by $${10}^{-2}$$. $$3\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{5}$$ Change to decimal form by moving the decimal five places right. $$300,000$$