Significant digits and easy average speed/ velocity questions

[Pruzhinkin]

Homework Statement

Here is a few examples where i am wondering as to how many significant digits to leave
3.5L/100km * 2279km = 79.765 ---> In this case am i supposed to round to 2 significant digits because of 3.5 which has two?

1.2L/100km * 63km = 0.756, i leave it as 0.76 right?

How about 31/90 = would i leave the answer as 0.3 or 0.34?
Also, if i am finding an answer for total time per mode of transport in this case, do i leave it as let's say 0.3 hours or convert it into 18min?

_____________________

Also, i know how to find average speed - total distance/ total time, but what if in this case it includes two segments in the total time -do i still do the total distance/ total time. I think it makes sense as that would basically be description of average speed.

Average velocity is found by total displacement/ total time
. I know that average velocity can be found by drawing a line and finding its slope but if i can see from the graph total displacement without finding the slope, can i just do the equation?

Homework Equations

Average speed = total distance/ total time
Average velocity = change in position/ change in time

The Attempt at a Solution

I think i basically explained everything under the "Problem Statement"
I am sorry that i am not completely using the template as i did not know how to formulate the question correctly. I understand that this is simple, but i am just getting confused - i can never move on until i know that i have everything figured out 100%. Thanks in advance, as this is really important

 

[PhanthomJay]

Homework Statement

Here is a few examples where i am wondering as to how many significant digits to leave
3.5L/100km * 2279km = 79.765 ---> In this case am i supposed to round to 2 significant digits because of 3.5 which has two?

100 in theory has just 1 significant figure..but in any case, you get 80 for the answer

1.2L/100km * 63km = 0.756, i leave it as 0.76 right?

0.8 is more likely correct, but any person of reason would accept 0.76

How about 31/90 = would i leave the answer as 0.3 or 0.34?

same reasoning as above...but I'd use 0.34, it makes more sense to me..

Also, if i am finding an answer for total time per mode of transport in this case, do i leave it as let's say 0.3 hours or convert it into 18min?

now you must use .34444(60) = 20.66 min, or the answer would be 21 seconds or 20.7 might be fine. Bottom line is that significant figure rules are not always to be applied universally...it depends on the problem...even a 5th grader knoews that 33/3 = 11 and not 10

_____________________

Also, i know how to find average speed - total distance/ total time, but what if in this case it includes two segments in the total time -do i still do the total distance/ total time. I think it makes sense as that would basically be description of average speed.

yes, correct

Average velocity is found by total displacement/ total time
. I know that average velocity can be found by drawing a line and finding its slope but if i can see from the graph total displacement without finding the slope, can i just do the equation?

well, sort of, find total displacement vector and divide by time...but direction is important...you must indicate the direction of the average velocity

 

[Pruzhinkin]

So do you think there is any reason to convert it to minutes? I do not know if i should or not as the question does not indicate whether it should be in hours or minutes. See the 31/90 is 31km/90km/h to find the total time per mode of transport. In the first cause you said that 0.34 is the correct answer, but when changing into minutes i am supposed to us 0.34444(60) which will give me 20.66 min. In your opinion should i leave the answer as hours or minutes? Also the main idea that your mentioning is that when converting into minutes i am supposed to use the exact number (e.g 0.34444 not 0.34), right?

Oh and if 100km was written as 100.0km it would have 3 significant digits?
And for 3.5L/100km * 2279km = 79.765 does 80 not feel to vague?
Or do i just leave it as 80 because of the one significant digit?

Also another quick question, for example i am finding average speed, and the distance is in km and time in minutes. Do i convert the minutes into seconds before i do the calculation, or should i convert km/min to km/h after all of the calculations.

Thanks for your awesome help:)

 

[PhanthomJay]

So do you think there is any reason to convert it to minutes? I do not know if i should or not as the question does not indicate whether it should be in hours or minutes. See the 31/90 is 31km/90km/h to find the total time per mode of transport. In the first cause you said that 0.34 is the correct answer, but when changing into minutes i am supposed to us 0.34444(60) which will give me 20.66 min. In your opinion should i leave the answer as hours or minutes?

Oh most people I suppose don't talk about tenths or hundredths of an hours, so I'd opt for minutes, and use 21 minutes as the answer.

Also the main idea that your mentioning is that when converting into minutes i am supposed to use the exact number (e.g 0.34444 not 0.34), right?

that's right, do the intermediate work to as many decimals as you can, then use sig figs and round off rules at the very end. Otherwrise, your error might be large (you'd get only 18 seconds instead of 21 if you used 0.3 hours instead of 0.344444hours; and you'd get 20 seconds instead of 21 if you used 0.34 hours instead of the 0.3444444444.

Also another quick question, for example i am finding average speed, and the distance is in km and time in minutes. Do i convert the minutes into seconds before i do the calculation, or should i convert km/min to km/h after all of the calculations.

Thanks for your awesome help:)

It doesn't much matter if you do all your intermediate calcs to a lot of decimal points until you get to the end. Suppose an object covers a total distance of 125 km in 55 minutes. Its average speed would be 125/55 = 2.2727 km/min, or that's 2.3 km/min rounded to 2 sig figs. If you wanted it in km/hr, then its 2.2727(60) = 136.36 km/hr, or to 2 sig figs, 140 km/hr. Now if you converted up front, it's (125)/(55/60) = 136.36 km/hr = 140 km/hr to 2 sig figs.

 

[Pruzhinkin]

Perfect, thank- you so much!

 

[tiny-tim]

Hi Pruzhinkin!

I disagree, I think it should be 2 sig figs in each case, because I think you should ignore the 100 km completely …

3.5L/100km * 2279km = 79.765 ---> In this case am i supposed to round to 2 significant digits because of 3.5 which has two?

1.2L/100km * 63km = 0.756, i leave it as 0.76 right?

The question is, how accurate is the 100 km supposed to be?

If someone ran 100 m in 11.3 seconds, would you work out the speed to 1 sig fig?

Of course not … the 100 may look like 1 sig fig, but it's almost certainly been measured extremely accurately (presumably at least as accurately as the stop-watch's accuracy justifies).

So you ignore it!

To put it another way, suppose your question said .035L/1km, would you treat that as two figures, one of which is "1" to 1 sig fig, or would you treat it as one figure ("3.5"), the units of which are L/km ?

As a matter of common-sense, you can safely assume that when the manufacturers (if they're telling the truth! ) measured the fuel consumption, they chose a distance measured to at least the accuracy required to justify the 2 sig figs in the published result.

How about 31/90 = would i leave the answer as 0.3 or 0.34?

Depends what the 90 is. If eg it's a reading on a car's milometer (what's the metric word for it? a kilometerometer? ), common-sense tells us that they give readings to the nearest unit.

(But if it's nautical miles, without the benefit of GPS, it probably is only 1 sig fig. )

Also, if i am finding an answer for total time per mode of transport in this case, do i leave it as let's say 0.3 hours or convert it into 18min?

I've no idea!

(btw, for sig figs in adding numbers, see Borek's post in https://www.physicsforums.com/showthread.php?t=441877")