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Chapter 1: Problem 15

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
A mathematician would add the numbers directly and say the answer is 43.4. A scientist, considering significant figures, would round the answer to the least precise measurement (in this case, no decimal places) and say the answer is 43. The scientist's answer accounts for the uncertainty and precision of the measurements, acknowledging that there is inherent uncertainty in the data.

Step by step solution

01

Find the sum of the numbers - Mathematician's answer

Add the two numbers: \(15.4 + 28 = 43.4\) So, a mathematician would say the answer is 43.4.
02

Estimate the sum with significant figures - Scientist's Answer

Here, the given numbers are 15.4 and 28. The first number has one decimal place, while the second number has no decimal places. A scientist would likely consider the significance of the decimal place in each number and round their answer accordingly. When adding numbers, the result should have the same number of decimal places as the least precise measurement. In this case, that would be the number 28, since it has no decimal places.
03

Round the sum to the appropriate number of significant figures

After calculating the sum of 43.4, we should round it to the nearest whole number since the least precise measurement has no decimal places. In this case, the sum rounded to the nearest whole number is: \(43.4 \approx 43\) So, a scientist would say the answer is 43.
04

Explain the reasoning behind the scientist's answer

A scientist's answer is different from a mathematician's answer because scientists want to account for the uncertainty and precision of the measurements given. In this case, only one number has a decimal place (15.4) while the other number has none (28). The scientist would use the concept of significant figures to ensure the result is expressed with the appropriate level of precision. In this context, using the number 43 as the sum reflects the level of precision in the original measurements and acknowledges that there is uncertainty in the data.

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