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Chapter 1: Problem 27

Calculate the following to the correct number of significant figures. Assume that all these numbers are measurements. (a) \(x=17.2+65.18-2.4\) (b) \(x=\frac{13.0217}{17.10}\) (c) \(x=(0.0061020)(2.0092)(1200.00)\) (d) \(x=0.0034+\frac{\sqrt{(0.0034)^{2}+4(1.000)\left(6.3 \times 10^{-4}\right)}}{(2)(1.000)}\)

Short Answer

Expert verified
Question: Determine the results of the following operations and make sure the final answer contains the correct number of significant figures: a) 17.2 + 65.18 - 2.4 b) 13.0217 ÷ 17.10 c) 0.0061020 × 2.0092 × 1200.00 d) (0.0034 ± √[(0.0034)² + 4 × 1.000 × (6.3 × 10⁻⁴)]) / 2(1.000) Answer: a) 80.0 b) 0.7623 c) 14.682 d) 0.0031

Step by step solution

01

Perform the addition and subtraction

Initially, perform the mathematical operations directly: 17.2 + 65.18 - 2.4 = 79.98
02

Correct for significant figures in addition and subtraction

The number 17.2 has the least decimal places (1 decimal place), so the final answer also needs to have 1 decimal place. Therefore, the result is 80.0. ##Part (b): Division##
03

Perform the division

Initially, perform the division directly: 13.0217 ÷ 17.10 = 0.762307603686636
04

Correct for significant figures in division

The number 17.10 has the least significant figures (4 significant figures), so the final answer also needs to have 4 significant figures. Therefore, the result is 0.7623. ##Part (c): Multiplication##
05

Perform the multiplication

Initially, perform the multiplication directly: 0.0061020 × 2.0092 × 1200.00 = 14.68158784
06

Correct for significant figures in multiplication

The number 2.0092 has the least significant figures (5 significant figures), so the final answer also needs to have 5 significant figures. Therefore, the result is 14.682. ##Part (d): A Complex Operation Involving Both Addition, Division, and Square Root##
07

Compute the square root term

First compute the square root part of the equation: sqrt[ (0.0034)² + 4 × 1.000 × (6.3 × 10⁻⁴) ] = 0.002818913
08

Perform the addition, division

Then add 0.0034 and divide by 2(1.000) => [0.0034 + 0.002818913] ÷ 2 = 0.003109457
09

Correct for significant figures

Here, the tricky part is defining the least significant figure. In this case, we follow the term with the least accurate figure, namely 0.0034, which has 2 significant figures. Therefore, the result should have 2 significant figures, and it comes out to 0.0031.

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