How Many Sig Figs Given Error Range?

[Cosmophile]

Homework Statement

"A calculator displays a result as 1.3250780 x10^7 kg. The estimated uncertainty in the result is +/- 2%. How many digits should be included when the result is written?"

Homework Equations

I'm not sure that there are any relevant equations here, aside from (maybe)

Actual result = Measured result + (Measured result)*(+/- 0.02)

The Attempt at a Solution

1.3250780x10^7 = 13250780

13250780*(0.02) = 265016 (rounding to nearest 1)
13240780 + 265016 =
13515795

Where I have bolded the numbers that do not change when the possible error is added to the measured result. Because I am only sure of these two numbers, does that mean that my number of significant figures should be 2?

 

[BvU]

Hi Cosmo,

I'm not sure that there are any relevant equations here

Perhaps not equations, but some rules could be mentioned.

An interesting question. Note that even the 2% is an estimate -- and the question doesn't reveal if that estimate is a rough estimate from say, squinting an eye at the scale from which the thirteen million is read off, or if it's an accurate estimate from calculating the standard deviation of a set of a hundred observations. On top of that, the question can be considered ambiguous: it's not clear if 'the result' can include reporting the error or not.

In the former case the answer is easy: (13.2 +/- 0.3) (13.3 +/- 0.3) kilotonne should both be considered reasonable, so three digits.
In the latter case things become really difficult: the tacit assumption is that the error is plus or minus one half of the last digit (i.e. 13 means between 12.5 and 13.5). Then two digits makes one lose accuracy unnecessarily. However, 13.3 would then mean 'in the range [13.25, 13.35]' and that's way too accurate.

My short reply would be: three digits. Main argument: the first digit of the result is a 1. Can you unravel the logic in that ?

 

[Cosmophile]

The question is certainly (hah) flawed, in my opinion. My physics class is being done entirely online, and it is questions like this which cause me to become irritated with the course. Especially when it is my performance in this class which will go on a transcript, and not my ability to solve more "physical" problems, like those posed in Kleppner & Kolenkow.

Woe is me, /plays world's smallest violin.

I've already submitted the assignment (I went with two significant figures, so whoops!) but I appreciate the write-up! I'll give it a moe diligent read when I'm finished with my other assignments. Thank you!