Confused about using rounding off numbers in physics

[jayadds]

Hi,

Let's say that a question is separated into two parts in which the latter part requires using the answer from the first part. Now, do I use that rounded off answer in the latter part or do I continue to use the exact number on my calculator for the latter part?

Many thanks.

 

[tiny-tim]

hi jayadds!

don't round it off completely, leave one or two extra significant figures

(you may need more, you may not need any … you'll find out when you get to the end )

 

[jayadds]

hi jayadds!

don't round it off completely, leave one or two extra significant figures

(you may need more, you may not need any … you'll find out when you get to the end )

Say that I did round it off to two significant figures, should I use THAT rounded off number or should I continue to use the "unrounded" number in the calculator for the next part of the question?

 

[tiny-tim]

i think i'd do it both ways, just to be on the safe side …

though i expect that they'd have set the question so that it makes no difference! ​

 

[physicsjock]

Usually I keep the numbers un-rounded until the end,

Then the rounding depends on the number of significant figures they have provided in the question.

If they have a question like, evaluate xy, x = 1.1 and y=1.23 you would get 1.353 but round it to 2 sig figs to get 1.4.

That's how they pushed us to do it in my first year physics anyway

 

[Hobin]

I agree with physicsjock. For example, if you have to evaluate xyz, where z = xy, y = 3x and x = 1.77 you should only round your your answer to three numbers at the *end* of the exercise. That's one of the reasons why it's most practical to use symbolic notation until the very end.

 

[MohammadG]

When you take an extra digit or two at the end of your answer and use that in your calculation you final answer should be accurate. You can then round off this answer to the necessary significant figures.

Using a rounded answer will give you a different result most of the time.

 

[jtbell]

Let's say that a question is separated into two parts in which the latter part requires using the answer from the first part. Now, do I use that rounded off answer in the latter part or do I continue to use the exact number on my calculator for the latter part?

When I write down the answer for the first part, I round it off appropriately; but I continue my calculations for the latter part using the unrounded result in the calculator.

For purposes of repeating the calculations in order to check them, it may be helpful to write down a couple of extra digits for the intermediate answer(s), but you should distinguish them clearly from the "official" digits of the answer, or write that version of the answer somewhere else.

 

[sophiecentaur]

Rounding off numbers is a non-linear operation. It is best to avoid this sort of thing - particularly when you follow it by subtracting two nearly equal large numbers. Rounding those numbers (one up and one down, perhaps) could turn the calculated relationship completely wrong!