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Chapter 1: Problem 22

Perform the following calculations; express each number and the answer in exponential form and with the appropriate number of significant figures. (a) \(\frac{320 \times 24.9}{0.080}=\) (b) \(\frac{432.7 \times 6.5 \times 0.002300}{62 \times 0.103}=\) (c) \(\frac{32.44+4.9-0.304}{82.94}=\) (d) \(\frac{8.002+0.3040}{13.4-0.066+1.02}=\)

Short Answer

Expert verified
The calculated results are (a) \(9.8 \times 10^4\), (b) \(2.48 \times 10^1\), (c) \(0.4461\), and (d) \(0.578\).

Step by step solution

01

Convert to Exponential Form and Calculate (a)

Convert \(320\), \(24.9\), and \(0.080\) to exponential form as \(3.20 \times 10^2\), \(2.49 \times 10^1\), and \(8.0 \times 10^{-2}\) respectively. Now perform the operation \(\frac{3.20 \times 10^2 \times 2.49 \times 10^1}{8.0 \times 10^{-2}}\) to get the answer which equals \(9.8 \times 10^4\).
02

Convert to Exponential Form and Calculate (b)

Convert \(432.7\), \(6.5\), \(0.002300\), \(62\), and \(0.103\) to exponential form as \(4.327 \times 10^2\), \(6.5 \times 10^0\), \(2.3 \times 10^{-3}\), \(6.2 \times 10^1\) and \(1.03 \times 10^{-1}\) respectively. Now perform the operation \(\frac{4.327 \times 10^2 \times 6.5 \times 10^0 \times 2.3 \times 10^{-3}}{6.2 \times 10^1 \times 1.03 \times 10^{-1}}\), which equals \(2.48 \times 10^1\) considering significant figures.
03

Add and Subtract before Division (c)

Add the values \(32.44\) and \(4.9\), and subtract \(0.304\) to get \(37.036\). Then divide this value by \(82.94\) to get \(0.4461\), considering number of significant figures.
04

Follow the sequence of operations (d)

Add \(8.002\) and \(0.3040\) to get \(8.306\), and subtract \(0.066\) from \(13.4\), then add \(1.02\) to the result, resulting \(14.36\). Now perform the operation \(\frac{8.306}{14.36}\) to get \(0.578\), considering the significant figures.

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