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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 5: Q. 5.48 (page 519)

Multiply or divide as indicated. Write answers in decimal form:
$鈸� (鈭� 3 脳 10^{鈭� 2}) (3 脳 10^{鈭� 1}) 鈸� \frac{8 脳 10^{4}}{2 脳 10^{鈭� 1}}$

Short Answer

Expert verified

The decimal form of the given expression is $(鈭� 3 脳 10^{鈭� 2}) (3 脳 10^{鈭� 1}) = 鈭� 0.009$

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

Step by step solution

01

Step 1. Given Information

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

$鈸� (鈭� 3 脳 10^{鈭� 2}) (3 脳 10^{鈭� 1}) 鈸� \frac{8 脳 10^{4}}{2 脳 10^{鈭� 1}}$

02

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

Use the Commutative Property to rearrange the factors.

$(鈭� 3 脳 10^{鈭� 2}) (3 脳 10^{鈭� 1}) = 鈭� 3 路 3 路 10^{鈭� 2} 路 10^{鈭� 1}$

Multiply.

$(鈭� 3 脳 10^{鈭� 2}) (3 脳 10^{鈭� 1}) = 鈭� 9 路 10^{鈭� 2 - 1} (鈭� 3 脳 10^{鈭� 2}) (3 脳 10^{鈭� 1}) = 鈭� 9 路 10^{鈭� 3}$

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

$(鈭� 3 脳 10^{鈭� 2}) (3 脳 10^{鈭� 1}) = 鈭� 9 路 \frac{1}{10^{3}} (鈭� 3 脳 10^{鈭� 2}) (3 脳 10^{鈭� 1}) = 鈭� 9 路 \frac{1}{1000} (鈭� 3 脳 10^{鈭� 2}) (3 脳 10^{鈭� 1}) = 鈭� 0.009$

03

Part (b) Step 1. The given expression is 8×1042×10−1

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

$\frac{8 脳 10^{4}}{2 脳 10^{鈭� 1}} = \frac{8}{2} 脳 \frac{10^{4}}{10^{鈭� 1}}$

Divide.

$\frac{8 脳 10^{4}}{2 脳 10^{鈭� 1}} = 4 脳 10^{4 + 1} \frac{8 脳 10^{4}}{2 脳 10^{鈭� 1}} = 4 脳 10^{5}$

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

$\frac{8 脳 10^{4}}{2 脳 10^{鈭� 1}} = 4, 00, 000$

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