Q16P Find the absolute and percent re... [FREE SOLUTION]

Chapter 3: Q16P (page 62)

Find the absolute and percent relative uncertainty and express each answer with a reasonable number of significant figures.
$a) 9.23 (卤 0.03) + 4.21 (卤 0.02) - 3.26 (卤 0.06) = ? b) 91.3 (卤 1.0) 脳 40.3 (卤 0.02) / 21.1 (卤 0.02) = ? c) [4.97 (卤 0.05) - 1.86 (卤 0.01)] / 21.1 (卤 0.02) = ? d) 2.0164 (卤 0.0008) + 1.233 (卤 0.002) + 4.61 (卤 0.01) = ? e) 2.0164 (卤 0.0008) 脳 10^{3} + 1.233 (卤 0.002) 脳 10^{2} + 4.61 (卤 0.01) 脳 10^{1} = ? f) {[3.14 (卤 0.05)]}^{1 / 3} = ? g) \log {[3.14 (卤 0.05)]}^{1 / 3} = ?$

Short Answer

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To calculate the absolute and percent relative uncertainty

Step by step solution

To calculate the absolute and percent relative uncertainty.

$a) 9.23 (卤 0.03) + 4.21 (卤 0.02) - 3.26 (卤 0.06) = 10.18 (卤 0.07 or 卤 0.07 %) b) 91.3 (卤 1.0) 脳 40.3 (卤 0.02) / 21.1 (卤 0.02) = 174 (卤 3 or 卤 2 %) or 174.4 (卤 2.7 or 卤 1.5 %) c) [4.97 (卤 0.05) - 1.86 (卤 0.01)] / 21.1 (卤 0.02) = 0.147 (卤 0.0003 or 卤 2 %) or 0.1474 (卤 0.0028) (卤 1.9 %) d) 2.0164 (卤 0.0008) + 1.233 (卤 0.002) + 4.61 (卤 0.01) = 7.86 (卤 0.01 or 卤 0.1 %) e) 2.0164 (卤 0.0008) 脳 10^{3} + 1.233 (卤 0.002) 脳 10^{2} + 4.61 (卤 0.01) 脳 10^{1} = 2185.8 (卤 0.8 or 0.04 %) f) [3.14 (卤 0.05)] a^{1 / 3} = 1.4643 (卤 0.0078 or 卤 0.53 %) g) \log {[3.14 (卤 0.05)]}^{1 / 3} = 0.49469 (0.0069 or 1.39 %)$

Formula to calculate the percent relative uncertainty

The percent relative uncertainty is calculated with the formula (e represents the $卤$ value)

$= \sqrt{e_{1}^{2} + e_{2}^{2} + e_{3}^{2}}$

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Short Answer

Step by step solution

To calculate the absolute and percent relative uncertainty.

Formula to calculate the percent relative uncertainty

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