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Chapter 1: Problem 15

Consider the addition of \(15.4\) to 28 . What would a mathemati- cian 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
A mathematician would say the answer is \(43.4\) after simply adding the numbers together. A scientist, considering significant figures, would also agree the answer is \(43.4\), since the least number of decimal places in the given numbers is one. Scientists use significant figures to maintain the precision of measurements, and in this case, the precision for both the mathematician and scientist is the same.

Step by step solution

01

Calculate the sum as a mathematician

To calculate the sum as a mathematician, simply add the two numbers: \(15.4 + 28\).
02

Perform the addition

Add the numbers together: \(15.4 + 28 = 43.4\). So, a mathematician would say the answer is \(43.4\).
03

Determine the significant figures in each number

Now let us look at the problem from a scientist's perspective, where significant figures are important. The first number, \(15.4\), has three significant figures, and the second number, \(28\), has two significant figures.
04

Perform the addition with significant figures in mind

When adding numbers and considering significant figures, the result should be rounded off to the least number of decimal places present in the numbers being added. In this case, \(28\) has no decimal places, while \(15.4\) has one. Thus, the answer should be rounded off to one decimal place.
05

Calculate the sum according to the rules of significant figures

Calculate the sum and round to one decimal place: \(15.4 + 28 = 43.4\), rounding to one decimal place gives us \(43.4\).
06

Explain the scientist's reasoning

The scientist's answer is also \(43.4\), which aligns with the mathematician's answer in this case. The reason scientists use significant figures is to ensure that the calculated results are consistent with the precision of the measurements being used in the calculation. By rounding off the answer to the least number of decimal places present in the numbers being added, the scientist is maintaining the precision of the measurements.

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Most popular questions from this chapter

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