# Not a homework - just a question about simply rounding off in physics

1. Jul 4, 2007

### Edwardo_Elric

ok
we had two significant figures as the least in our given
so what i did was to calculate the speed of the airplane....
my result is 52.5m/s.... i round it to two significant figures which is 53m/s

but our proff earlier wrote the answer in the blackboard 52.5m/s and considered it as just |V| = 52m/s...

is rounding off in physics different? because im really certain that .5 can be rounded off to one ... and besides i checked it here http://www.gomath.com/algebra/round.php [Broken] and its really 53

Last edited by a moderator: May 3, 2017
2. Jul 4, 2007

### cristo

Staff Emeritus
No, your teacher probably just made a mistake. 52.5 to two significant figures is equal to 53.

3. Jul 4, 2007

### George Jones

Staff Emeritus
Was the result exactly 52.5? If not, then, to 4 significant figures, what is the answer?

What I'm getting at is that, for example, 52.47 "rounds" to both 53.5 and 52, depending on how may digits are kept.

4. Jul 4, 2007

### Staff: Mentor

rounding off rules

Strictly speaking, your teacher is correct. According to current thinking, if the first digit to be dropped is 5, and it's followed by all zeroes (or nothing), then you only round up if the preceding digit is odd. (This is supposed to be more statistically valid than the old rule--that I admit I still follow mostly--of rounding up whenever the first digit to be dropped is 5.)

Do a search on "rounding off rules" and you find lots of sites describing this. Here's one: http://www.hartnell.cc.ca.us/faculty/shovde/chem22s/roundingrules.htm" [Broken]

More importantly: Was the answer really 52.5? To how many significant digits?

Last edited by a moderator: May 3, 2017
5. Jul 4, 2007

### cristo

Staff Emeritus
Wow, that's something I've never come across in all my years of studying maths! Still, though, I'm not sure whether a physics teacher would employ this "round to even" method when teaching a class, since the statistical advantage of the method will be zero in this case.

Perhaps the OP should ask which method of rounding the teacher is using (both for piece of mind, and to avoid getting the "incorrect" answer in future exams for this course).

Last edited by a moderator: May 3, 2017
6. Jul 4, 2007

### George Jones

Staff Emeritus
I wasn't taught this when I was in school, but, after reading your post, I remembered that a couple of years ago, someone told this rule.

I meant to write 52.5, not 53.3.

7. Jul 4, 2007

### Edwardo_Elric

heres the problem:
An airplane travels 480 m(thats 2 significant figures) down the runway before taking off. It starts from rest, moves with constant acceleration, and becomes airborne in 16.0s What is its speed, in m/s, when it takes off?

So the rule says that when you multiply it must be with the least significant figure... 52.5m/s round it off to two....

And really thanks for all the replies guys
it means that I have to search him for consultation hours..

omg is that true the preceding digit applies? didnt know that

Last edited: Jul 4, 2007
8. Jul 4, 2007

### Staff: Mentor

The number of significant figures in 480 m is ambiguous (unless they tell you, of course!). Written as 480, it should be 2 sig figs as you state. If they meant to show 3 sig figs, it should be written as 4.80 *10^2. But 480 could mean 3 sig figs, if the author was sloppy.

OK... so where do you get the 52.5 m/s??

9. Jul 4, 2007

### George Jones

Staff Emeritus
420 m instead of 480 m?

10. Jul 4, 2007

### nrqed

I have learned differently. I have learned that in a physics context, only significant figures were shown in a problem, so that 480 m really means three sig figs. That if only two sig figs were intended, it should have been written as 4.8 x 10^2 m. I guess it shows that there is no uniformity in the way it is taught.

11. Jul 4, 2007

### cepheid

Staff Emeritus
No information is given about the precision of the measuring instrument used or the resulting uncertainty in the measurement. As a result, it's really hard to say what was meant by 480 m and how many sig figs *ought* to be used to represent the message. If I assumed that we were measuring down to the nearest metre or something, then I'd agree with nrqed: 3 sig figs.

12. Aug 28, 2011

### JDoolin

Re: rounding off rules

Interesting document. If I know that someone is using this method, and I see they have written 21.4, then I know that the actual number is between 21.35, and 21.45 inclusive. But if I see 21.5, then I know the actual number is somewhere between 21.45 and 21.55 exclusive. Is that the general intention?

Last edited by a moderator: May 5, 2017