Rounding Homework Answers: Tips for GCSE and Below | Joe's Math Dilemma"

[joe465]

Homework Statement

Do you round an answer up as you go along in a problem or do you use the full until the last final answer of the problem. What happens when you calculate an angle, do you round to the nearest degree or can it still be allowed as a decimal?

Sorry this question goes back to GCSE and below but maths never was my strong point.

Thanks, Joe

 

[PeterO]

Homework Statement

Do you round an answer up as you go along in a problem or do you use the full until the last final answer of the problem. What happens when you calculate an angle, do you round to the nearest degree or can it still be allowed as a decimal?

Sorry this question goes back to GCSE and below but maths never was my strong point.

Thanks, Joe

You should only round the number at the end. Decimal angles should be just acceptable as degrees and minutes - unless the question requests one method specifically.

 

[joe465]

Thanks for your reply, the only reason i ask is because an answer can differ so much just by rounding/not rouding the numbers

 

[kuruman]

Thanks for your reply, the only reason i ask is because an answer can differ so much just by rounding/not rouding the numbers

Ideally, you do not round at all; you derive a symbolic expression for what the problem is asking, then put in the numbers at the very end. If you must calculate intermediate numbers, then you should carry through two or three extra decimals and round at the very end. This will avoid excessive propagation of errors.

 

[JDoolin]

Excellent. There's a current thread on a topic I was wondering about. However, I don't think it's a stupid question. It seems to me a very good question.

Since angles are cyclic, there is no more precision in the angle 210.33° than there is in the angle 0.33°. However, the first angle supposedly has five significant digits, and the other angle has only 2 significant digits.

If I were to round 210.33° to two significant digits, that represents 210 ± 5°, whereas an angle of 0.33° is accurate to ± .005°

 

[JDoolin]

A textbook I am using this semester asks for a change from cartesian coordinates
(x,y)=(-5.00,12.00) to polar coordinates.

This forms an obtuse triangle, so it is atan(-12/5)±180 = 112.6198649°

Since the problem is multiple choice, it is clear that the book wants 113° but I have some doubts about that. Why should an answer in the first or fourth quadrant deserve precision down to 0.1 degrees, while an answer in portions of the second and third quandrant deserve only precision to 1 degree?

 

[JDoolin]

Another question on rounding I have:

If I have a measurement of 136.52480, but the "estimated uncertainty" is 2, how many significant digits is the result?

I'm sure this somehow relates to a confidence interval of 134.52480 ≤ x ≤ 138.52480

What do the words "estimated uncertainty" mean in statistical language? Does the "estimated uncertainty" correspond to a 1-sigma (68.26%) confidence interval?

So if I say that this is 3 significant figures: 136; is that basically saying the number is between [135.5 , 136.5) which is more precise than the confidence interval actually is, (but misses the center) or should I say the number has 2 significant figures; 140 and is between [135 , 145) which is less precise than it actually is, but also does not fully contain the uncertainty interval?

I think maybe the best answer would be to keep one significant figure beyond the "estimated uncertainty" and write 132.5 ± 2. Then it is clear where your data is centered, and how certain you are of it. (Except that I still don't know whether it is a one-sigma confidence interval or a 95% CI or whatever.)