# Significant Figures and speed of a runner (1 Viewer)

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#### Bohring

1. The problem statement, all variables and given/known data

Calculate the speed of the runner.

Times, measured to nearest 5 seconds: 95, 100, 85, 80 seconds.
Mean Time: 90 seconds.

Distance: 200m

2. Relevant equations
Speed = Distance/Time

3. The attempt at a solution
Speed = Distance/Time = 200/90 = 2.2222222222 ms-1

Not sure how many significant figures I should put my answer to, though?
Is it just 2 ms-1, as the times are to 0dp, or is it 2.2 ms-1, as the least accurate time is to 2 sig fig?

Cheers!

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#### PhanthomJay

Homework Helper
Gold Member
1. The problem statement, all variables and given/known data

Calculate the speed of the runner.

Times, measured to nearest 5 seconds: 95, 100, 85, 80 seconds.
Mean Time: 90 seconds.

Distance: 200m

2. Relevant equations
Speed = Distance/Time

3. The attempt at a solution
Speed = Distance/Time = 200/90 = 2.2222222222 ms-1

Not sure how many significant figures I should put my answer to, though?
Is it just 2 ms-1, as the times are to 0dp, or is it 2.2 ms-1, as the least accurate time is to 2 sig fig?

Cheers!
Significant figure rules are sometimes confusing, but since the least number of sig figures is one (both 200 and 90 have just one significant figure), then the answer is 2 m/s.

#### tiny-tim

Homework Helper
Hi jay! Significant figure rules are sometimes confusing, but since the least number of sig figures is one (both 200 and 90 have just one significant figure), then the answer is 2 m/s.
Are you sure?

I get very confused by the sig figs rules (which is why I waited for someone else to reply first ), but does it matter about 200 and 90 having one sig fig?

The 200m is presumably on a measured track, and those tend to be accurate to within a cm or so.

And the 90 is the exact mean of the four given times, so it's not rounded at all.

It seems to me (applying common-sense rather than the rules) that since the time is "measured to nearest 5 seconds", it's accurate to about 1 in 20, which would be about 0.1 in 2.222… , giving an answer of 2.2.

And the individual speeds (using only one time each) would range from 2.0 exactly to 2.5 exactly, so choosing 2 as the mean speed seems to have lost a lot of information.

Anyone else got any ideas? #### PhanthomJay

Homework Helper
Gold Member
I changed my mind . As you noted, the runner's speed varies from 2 m/s (at 100 sec) to 2.5 m/s (at 80 sec); that wouldn't be right to call the runner's speed 2 m/s. So I would say you are correct, 2.2 m/s would be the answer. Significant figures is not my forte, that's for sure...common sense makes more sense #### tatiana

The most number of sig figs in this problem is 3 there fore your answer should be rounded to 2 sig figs also. If your answer is correct then your would answer should be 2.2. Even though i was taught hat there are no significant figures in physics only in chem?

#### Bohring

Thanks for your help everyone! I'm normally okay with things like this, but the more I thought about it, the more I got confused!

I was always taught to put your answer to the same number of sig figs as your least accurate piece of data. In this case, it's 1 sig fig, but as you say, it seems like you're losing a lot of information!

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