Significant Figures Homework: Converting Time from Min to Hrs

In summary, the conversion factor for minutes to hours is 1/60 hr, and any uncertainties should be quoted to the same number of decimal places as the answer. Additionally, when using data to calculate a result, the significant figure rules should be followed to maintain accuracy.
  • #1
Jam51
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0

Homework Statement


I am starting to confuse myself with the proper use of SF. I am to convert time from minutes to hours, keeping in mind proper SF

Homework Equations


conversion factor: 1 min = 1/60 hr

The Attempt at a Solution



The timing error is +/- 0.2 (1SF) = 0.003hr (1SF)

20.0 min (3 SF) = 0.333 hr (3 SF), but the conversion factor has 1 SF? would my answer be 0.3 hr? I'm confused because now I have varying decimal places and when I say 0.3 +/- 0.003 hr doesn't seem corect at all because when adding or subtracting I would drop the 0.003 therefore never being relevant?

Please help.
 
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  • #2
Conversion factors that are defined rather than measured are taken to have infinite precision. Thus the constant "60" in the conversion of minutes to hours or vice versa is exact.
 
  • #3
Ok, so if I am converting 20.0 min using the "infinite" 60, the answer would reduce to the 3SF from the minute value?
 
  • #4
Jam51 said:

Homework Statement


I am starting to confuse myself with the proper use of SF. I am to convert time from minutes to hours, keeping in mind proper SF

Homework Equations


conversion factor: 1 min = 1/60 hr

The Attempt at a Solution



The timing error is +/- 0.2 (1SF) = 0.003hr (1SF)

20.0 min (3 SF) = 0.333 hr (3 SF), but the conversion factor has 1 SF? would my answer be 0.3 hr? I'm confused because now I have varying decimal places and when I say 0.3 +/- 0.003 hr doesn't seem corect at all because when adding or subtracting I would drop the 0.003 therefore never being relevant?

Please help.

As a general rule, you need to quote your answer to the same number of decimal places as your uncertainty.

If you have an uncertainty of 0.55 on 10, I would expect to see ##x = (\mathrm{10.00} \pm \mathrm{0.55}) \mathrm{units}##
 
  • #5
Right. Just so I am understanding that correctly.

In minutes my uncertainty is +/- 0.2, therefore on 20.0 minutes, it would remain as 20.0 +/- 0.2 min (both have the same amount of decimal places)
In hours the uncertainty would be +/- 0.003, where 20.0 min = 0.333 hr, would be 0.333 +/- 0.003 hr.

Now what if distance comes to play and it was only one decimal place? Am I still ok to leave the above as 3 decimal places if i intend to plot d v t on a graph?
 
  • #6
Jam51 said:
Now what if distance comes to play and it was only one decimal place? Am I still ok to leave the above as 3 decimal places if i intend to plot d v t on a graph?
As long as the different data is kept separate they keep their own significant figures and accuracy. So in a plot where the data are on separate axes they have their separate uncertainties and significant figures. If you use the data to calculate the slope of the resulting curve or the area under the curve, then you are "mixing" the data and you need to heed the significant figure rules for any results.
 
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Likes Jam51 and gracy
  • #7
Thank you :smile:
 

What are significant figures and why are they important in converting time from minutes to hours?

Significant figures represent the precision or accuracy of a measurement. In converting time from minutes to hours, it is important to use the correct number of significant figures to maintain accuracy and avoid rounding errors.

How do I determine the number of significant figures in a given time measurement in minutes?

The rule for determining significant figures is to count all non-zero digits and any zeros between them. For example, in 45.30 minutes, there are four significant figures.

What is the conversion factor for minutes to hours?

The conversion factor for minutes to hours is 1 minute = 0.01667 hours. This means that to convert minutes to hours, you would multiply the number of minutes by 0.01667.

Can I round my final answer to the nearest minute?

No, when converting time from minutes to hours, it is important to maintain the appropriate number of significant figures. Rounding to the nearest minute can result in a less precise answer.

What are some common mistakes to avoid when converting time from minutes to hours?

Some common mistakes to avoid include forgetting to convert the units, using the wrong conversion factor, and rounding the final answer too soon. It is also important to pay attention to significant figures and use the appropriate number in the final answer.

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