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Chapter 1: Problem 17

Consider the addition of \(15.4\) to 28 . What would a mathematician say the answer is? What would a scientist say? Justify the scientist's answer, not merely citing the rule, but explaining it.

Short Answer

Expert verified
The mathematician's answer to the addition of \(15.4\) and \(28\) would be \(43.4\), while the scientist's answer would be \(43\). The scientist's answer considers the significant figures involved in the measurements, acknowledging that the answer can't have more precision than the least precise measurement. This approach takes into account the accuracy and uncertainty of the measurements.

Step by step solution

01

Adding the numbers

To begin, we will add the two numbers together: \(15.4 + 28 = 43.4\)
02

Understanding the mathematician's answer

A mathematician would simply report the answer we calculated in Step 1, which is: \(43.4\)
03

Understanding significant figures

To find the scientist's answer, we need to understand significant figures. Significant figures represent the number of known digits in a measurement, with the idea that the more significant figures, the more accurate a measurement is. In this problem, we have the following numbers of significant figures: - 15.4 has three significant figures - 28 has two significant figures When performing mathematical operations, we need to follow the rules for significant figures in order to maintain the accuracy of the measurements.
04

Applying the significant figures rules in addition

In addition, the answer should have the same number of decimal places as the least precise measurement (the one with the least number of decimal places). In this case, the least precise measurement is 28, which has no decimal places. Therefore, the scientist's answer should also have no decimal places.
05

Calculate the scientist's answer

To find the scientist's answer, we'll round the mathematician's answer to the nearest whole number: \(43.4 \approx 43\)
06

Explaining the scientist's answer

The scientist's answer is different from the mathematician's answer because the scientist is considering the precision of the measurements. By limiting the answer to the same precision as the least precise measurement (in this case, 28), we're acknowledging that the answer can't have more precision than the least precise measurement involved. This approach best represents the accuracy and uncertainty of the measurement. So, the mathematician's answer is \(43.4\), while the scientist's answer is \(43\).

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Most popular questions from this chapter

The active ingredient of aspirin tablets is acetylsalicylic acid, which has a density of \(1.4 \mathrm{~g} / \mathrm{cm}^{3} .\) In a lab class, a student used paper chromatography to isolate another common ingredient of headache remedies. The isolated sample had a mass of \(0.384 \mathrm{~g}\) and a volume of \(0.32 \mathrm{~cm}^{3}\). Given the data in the following table, what was the other ingredient in the headache remedy? $$ \begin{array}{l} \text { Density Values for Potential } \\ \text { Headache Remedies } \\ \begin{array}{lc} \text { Compound } & \text { Density }\left(\mathrm{g} / \mathrm{cm}^{3}\right) \\ \hline \text { White table sugar } & 0.70 \\ \text { Caffeine } & 1.2 \\ \text { Acetylsalicylic acid } & 1.4 \\ \text { Sodium chloride } & 2.2 \\ \hline \end{array} \end{array} $$

A star is estimated to have a mass of \(2 \times 10^{36} \mathrm{~kg}\). Assuming it to be a sphere of average radius \(7.0 \times 10^{5} \mathrm{~km}\), calculate the average density of the star in units of grams per cubic centimeter.

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A rectangular block has dimensions \(2.9 \mathrm{~cm} \times 3.5 \mathrm{~cm} \times 10.0 \mathrm{~cm}\). The mass of the block is \(615.0 \mathrm{~g}\). What are the volume and density of the block?
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