Calculating Uncertainty when Converting Time

[ELLE_AW]

Homework Statement

The problem asks to convert time in minutes to time in hours, and to also calculate the uncertainty for the time in hours.Specifically 10 minutes +/- 0.2min being converted to hours with uncertainty.

2. Homework Equations & 3.The attempt at a solution
conversion of time:
10.0 min x 1h/60 min = 0.167h

uncertainty of time in hours:
- 1/60 is a conversion factor, and has an uncertainty of zero
- When multiplying, you're supposed to calculate the percent uncertainty of each measure and add them up to get the percent uncertainty of the product. Then, you can apply that percent uncertainty to the product to see what the uncertainty would be.

So I did the following:

time in minutes ± 0.2 (min), therefore 0.2min/10min = 0.02%

1/60 is a conversion factor, and has zero uncertainty

Therefore, 0.02% + 0% = 0.02%, which can now be applied to the product of the sample calculation for time in hours:

0.167 x 0.02% = 0.0000334

so time in hours = 0.167 +/- 0.0000334

This answer just doesn't make sense to me though. First of all the number of decimal places between the measurement and the uncertainty don't match or even come close.

I feel like a more likely answer would be to just convert 0.2 min (the uncertainty of time in minutes) to hours ( 0.2 min x 1h/60min = 0.003h) and then just have that be the uncertainty for hours, since the conversion factor does not play any role here.

So my final answer would be Time in Hours:
0.167 h +/- 0.003I've BOLDED both of my answers. Which one do you guys think makes more sense and why?

Thanks

 

[Orodruin]

0.2 is 2 % of 10, not 0.02 %.

 

[ELLE_AW]

0.2 is 2 % of 10, not 0.02 %.

Hahaha, oh wow. I'm definitely tired today. That explains everything. Thanks!

 

[Orodruin]

Sometimes you stare at a problem for so long that the obvious solution becomes invisible to you...