Significant figures in seconds to hours calculation

[RossH]

SOLVED: Significant figures in seconds to hours calculation

Homework Statement

Not exactly a problem, but if I have minutes/seconds and am changing to hours, how many significant figures are there? For example: 29 minutes 57 seconds =0.499166667 hours needs ? significant figures.

The Attempt at a Solution

Well, a second to 1/3600 hours. Therefore, I think I might want to measure to a precision of one ten-thousandth of an hour, or possibly 1/1000 hours. I'm not sure which. I know that the minutes doesn't affect the calculation, and I know that the unit conversion is considered to have infinite sig figs.

 

[gneill]

The implication is that the original value is accurate to +/- 1 second. If the converted value is to have a similar level of precision, and 1s = 0.00028 hr, then it looks like you'll want four decimal places and the last place will be taken as +/- 3.

 

[RossH]

The implication is that the original value is accurate to +/- 1 second. If the converted value is to have a similar level of precision, and 1s = 0.00028 hr, then it looks like you'll want four decimal places and the last place will be taken as +/- 3.

Thanks!

 

[Redbelly98]

I agree the value is accurate to the nearest 1 second, but would approach it differently. If you convert the 29 minutes 57 seconds to seconds, that's 60·29+57 seconds or 1767 seconds. That's 4 significant figures -- which for this problem (0.4991... hours) means to the 4th decimal place in agreement with what gneill said.

 

[asteriatic]

Your thinking is on the right track. When converting between units, the conversion factor is considered to have infinite significant figures. In this case, the conversion factor is 1/3600 hours. Therefore, the significant figures in the final answer will be determined by the number of significant figures in the original value of 29 minutes 57 seconds. Since this value has 4 significant figures, the final answer should also be reported with 4 significant figures, giving an answer of 0.4992 hours.