Mathematics » Introducing Polynomials » Integer Exponents and Scientific Notation

Multiplying and Dividing Using Scientific Notation

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.\(300,000\)

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