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Chapter 1: Problem 28

Calculate the following to the correct number of significant figures. (a) \(x=128.5+2116.44-2244.47\) (b) \(x=0.004010 \times 2.0000 \times 50054\) (c) \(x=\frac{12.6+0.3+256.5}{1003.7}\) (d) \(x=\frac{12.20-\sqrt{1.60+4(0.36)}}{1.3409}\)

Short Answer

Expert verified
Question: Calculate the value of x for each given mathematical expression, taking into account significant figures: (a) \(x = 128.5 + 2116.44 - 2244.47\) (b) \(x = 0.004010 \times 2.0000 \times 50054\) (c) \(x = \frac{12.6 + 0.3 + 256.5}{1003.7}\) (d) \(x = \frac{12.20 - \sqrt{1.60 + 4(0.36)}}{1.3409}\) Answer: (a) \(x = 0.47\) (b) \(x = 40.11\) (c) \(x = 0.268\) (d) \(x = 7.797\)

Step by step solution

01

Part (a) - Calculate x

To calculate x, perform the arithmetic operation by adding 128.5 and 2116.44, and then subtracting 2244.47 from the result: \(x = 128.5 + 2116.44 - 2244.47\) Now, apply the rules for significant figures for addition and subtraction operations. The result must have the same number of decimal places as the least precise number involved in the operation. In this case, the least precise number has one decimal place (128.5), so the final answer should have one decimal place as well. \(x = 0.47\)
02

Part (b) - Calculate x

Multiply the three numbers: \(x = 0.004010 \times 2.0000 \times 50054\) Apply the rules for significant figures for multiplication operations. The result must have the same number of significant figures as the least precise number involved in the operation. In this case, the least precise number has four significant figures (0.004010), so the final answer should have four significant figures as well. \(x = 40.11\)
03

Part (c) - Calculate x

First, add the numbers in the numerator: \(12.6 + 0.3 + 256.5 = 269.4\) Now, divide the sum by the denominator: \(x = \frac{269.4}{1003.7}\) For division, apply the rules for significant figures. The result must have the same number of significant figures as the least precise number involved in the operation. In this case, the least precise number has three significant figures (12.6), so the final answer should have three significant figures as well. \(x = 0.268\)
04

Part (d) - Calculate x

First, calculate the expression inside the square root: \(1.60 + 4(0.36) = 1.60 + 1.44 = 3.04\) Next, take the square root of the result: \(\sqrt{3.04} = 1.743\) Now, subtract the square root from the numerator: \(12.20 - 1.743 = 10.457\) Finally, divide the result by the denominator: \(x = \frac{10.457}{1.3409}\) Apply the rules for significant figures for division operations. The result must have the same number of significant figures as the least precise number involved in the operation. In this case, the least precise number has four significant figures (12.20), so the final answer should have four significant figures as well. \(x = 7.797\)

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