# Significant Figures and speed of a runner

• Bohring
In summary: I guess it depends on how strict your teacher is with sig figs, but I think I'll go with 2 sig figs as well. Thanks again for your help!In summary, the runner's speed can be calculated as 2.2 m/s, taking into account the least accurate time measurement of 1 sig fig. However, some may argue that the individual times and distance measurement are more precise, suggesting a value of 2.2222222222 m/s. Ultimately, the number of significant figures used may vary depending on the level of strictness in applying sig fig rules.
Bohring

## Homework Statement

Calculate the speed of the runner.

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

Distance: 200m

## Homework Equations

Speed = Distance/Time

## 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!

Last edited:
tomself1 said:

## Homework Statement

Calculate the speed of the runner.

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

Distance: 200m

## Homework Equations

Speed = Distance/Time

## 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.

Hi jay!
PhanthomJay said:
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?

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

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?

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!

Last edited by a moderator:

## What are significant figures and why are they important?

Significant figures are a way of representing the precision of a measurement. They show the number of digits that are known with certainty and help to avoid misleading results. Significant figures are important because they allow for accurate and consistent communication of scientific data.

## How do you determine the number of significant figures in a measurement?

The rules for determining significant figures are as follows:
- All non-zero digits are significant
- Zeros between two significant digits are significant
- Zeros to the left of the first non-zero digit are not significant
- Zeros to the right of the last non-zero digit are significant if there is a decimal point
- Zeros to the right of the last non-zero digit may or may not be significant if there is no decimal point

## What is the significance of significant figures in scientific calculations?

When performing calculations with measurements, the result should have the same number of significant figures as the measurement with the least number of significant figures. This ensures that the result is not more precise than the original measurements and avoids false precision.

## How does the speed of a runner relate to significant figures?

The speed of a runner can be measured using various instruments, such as a stopwatch or a speedometer. The number of significant figures in the measurement of the runner's speed will depend on the precision of the instrument used. For example, if a stopwatch measures to the nearest 0.01 seconds, the speed measurement should have two significant figures.

## How do you round a measurement to the correct number of significant figures?

To round a measurement to the correct number of significant figures, follow these steps:
1. Identify the digit to be rounded
2. Look at the digit to the right of the identified digit
3. If the digit is 5 or greater, round up the identified digit
4. If the digit is less than 5, leave the identified digit unchanged
5. If the digit is exactly 5, round up if the preceding digit is odd and leave unchanged if the preceding digit is even

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