Phy 121
Your 'question form' report has been received. Scroll down through the document to see any comments I might have inserted, and my final comment at the end.
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Assignment 2 Open Query you write:
Question: Give your solution to the following, which should be in your notes: Find the approximate uncertainty in the area of a circle given that its radius is 2.8 * 10^4 cm.
STUDENT COMMENT: I understand how squaring the problem increases uncertainty and I understand the concept of
a range of uncertainty but I am having trouble figuring out how the range of 2.75 * 10^4 and 2.85*10^4 were established
for the initial uncertainties in radius.
INSTRUCTOR RESPONSE:
The key is the first sentence of the given solution:
'Radius 2.8 * 10^4 cm means that the radius is between 2.75 * 10^4 cm and 2.85 * 10^4 cm.'
You know this because you know that any number which is at least 2.75, and less than 2.85, rounds to 2.8.
Ignoring the 10^4 for the moment, and concentrating only on the 2.8:
Since the given number is 2.8, with only two significant figures, all you know is that when rounded to two significant figures the quantity is 2.8. So all you know is that it's between 2.75 and 2.85.
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This makes perfect sense to me as for why that is the uncertainty; however, according to P. 6 of the text:
Often teh uncertainty in a measured value is not specified explicitly. In such cases, the uncertainty is generally assumed to be one or a few units in the last digit specified. For example, if a length is given as 8.8 cm, the uncertainty is assumed to be about 0.1 cm or 0.2 cm. It is important in this case that you do not write 8.80 cm,for this implies an uncertainty on the order of 0.01 cm
To me this is saying that the uncertainty is considered to be +- 1 or 2 of the last place specified.
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The book states that this is 'generally assumed'. The assumptions made in the given solution are slightly different than those in the text.
You can use any reasonable set of assumptions, as you find them appropriate to the situation. The assumptions of the given solution might be appropriate in some cases, those of the text in others.
I prefer to have you make reasonable judgements, as opposed to following hard and fast rules. Difference in these judgements can of course be discussed and questioned (that's part of the process of science).