How Should Time and Distance Uncertainties Affect Calculations in Physics Labs?

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In a physics lab scenario involving a car traveling from Point A to Point B, uncertainties in time and distance measurements are discussed. The distance uncertainty is estimated at ±0.1 km, while the timing error is ±0.2 min, leading to confusion over significant figures in calculations. The discussion emphasizes the importance of maintaining consistent decimal places for both median values and their associated error margins. There is a suggestion that rounding error ranges up may be beneficial for accuracy. Overall, the focus is on how to appropriately convert and present time measurements while adhering to significant figure rules to avoid losing points.
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Homework Statement


This is a lab question. I'll summarize with key information.

Car traveling from Point A to Point B. You record the time and distance.

"Since the odometer gave the distance within 100 m, you estimated the uncertainty in d to be (Δd = ±0.1 km). Regarding the time, even though you did your best to take the meter reading at equal time intervals of 10 minutes, you still estimated a timing error of about 12 seconds (or Δtm = ±0.2 min)."

Here is the table they give you and we have to fill in the time in hours
KCJfOZO.png


Homework Equations


1min = 1/60 hrs

The Attempt at a Solution


At first, I look at the 12 seconds as 2 sig figs so my Δth should also be 2 sig figs... thus Δth = ±3.3E-3 hrs

I'm confused about the data they've given. 10.0 is 3 sig figs and 170.0 is 4 sig figs. So would my
10.0 ± 0.2 min become 1.67E-1 ± 3.3E-3 hrs
170.0 ±0.2 min become 2.833 ± 3.3E-3 hrs
 
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Since you are quoting error ranges for the data, it is not a sin to have more digits than can strictly be justified. (It matters more when error ranges are not stated because in that case the reader infers the error range from the significant digits shown.)
But I do think it is wrong to have the error margin and the median terminating at different decimal positions. If you are going to quote the error range down to thousandths of an hour then you should do the same for median values.
 
The lab deals with uncertainty and significant figures so I can't have more than I need because I'll lose points. Based on the information given, what do you guys think should my 10.0 min and 170.0 min be converted to?
 
John_tawil said:
The lab deals with uncertainty and significant figures so I can't have more than I need because I'll lose points. Based on the information given, what do you guys think should my 10.0 min and 170.0 min be converted to?
Then I fear you are dealing with the opinions of your teacher more than with any real logic. I can't comment further without knowing exactly what you have been taught.
However, I do stand by my second observation, that the last digit should be at the same decimal place in median and error.
Edit: one more thought... arguably, you should always round the error range up, so 1/3 becomes 0.34, say, not 0.33.
 
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