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Find the absolute uncertainty of the following calculation, and express the answer to the proper number of significant figures. 12.34(+0.04)+178.1(10.2) - 18.493(±0.002) a) 172.01 (±0.2) b) 172.0 (+0.2) c) 172.010 (+0.242) d) 172.01 (+ 0.24)
Accepted Answer
The correct answer is B) 172.0 (+0.2). Here's how to determine the absolute uncertainty:
1. Calculate the sum: 12.34 + 178.1 - 18.493 = 172.0
2. Add the absolute uncertainties: 0.04 + 10.2 + 0.002 = 10.242
3. Round the absolute uncertainty to the same number of decimal places as the least precise measurement: The least precise measurement is 178.1 (with one decimal place), so the absolute uncertainty rounds to 0.2.
4. Express the final answer with the correct number of significant figures: Since the uncertainty is in the tenths place, the final answer should also be rounded to the tenths place. Therefore, the answer is 172.0 (+0.2).
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