There are exactly 60 seconds in a minute, there are exactly 60 minutes in an hour, there are exactly 24 hours in a mean solar day, and there are 365.24 solar days in a solar year. Find the number of seconds in a solar year.

I thought I had the right answer with 31556736 but its not...it also has to be in sig figs

Thanks!!

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The above answers are incorrect. Here you want to use FIVE significant figures. The reason for this is because conversion factors do NOT get factored into the significant figure rules. Since even your question states "there are EXACTLY....." you can assume that this is NOT limiting your significant figures (which makes sense, because seconds and minutes and hours are human-made time intervals.)

The year (the time it takes the earth to go around the sun) is NOT an interval that is made up arbitrarily by humans (hence why there is a decimal place in the conversion). THIS is your limiting factor, so your answer will have 5 significant figures.

3.1557x10^7

Edit: Redbeardthegiant's answer wasn't there when I started typing this, his answer is correct, except for a minor rounding error.

• Anonymous

When multiplying with significant figures, we use the number of digits from the least precise number. However, since the problem states that there are exactly 60 seconds in a minute, that becomes a definition, not a measurement, so we don't need to worry about the number of sig. dig. The same is true for the number of minutes in an hour and the number of hours in a day. However, 365.24 is a rounded number, so we would use the number of sig. dig in that number for our answer. Since 365.24 has 5 sig. dig., the answer would have 5 sig. dig., so 3.1557 x 10^7.

Daniel is wrong about the significant figures.

Normally I would agree that just the number 60 has one sig fig.

BUT we know that there are exactly 60 seconds per minute, not 61, not 59, and not even 59.999999 - so we have many more effective sigfigs than usual - the word 'exactly' is the key here.

Same for 24.

So the 365.24 is your limiting sigfig number.

Therefore your answer is 31556736 at 5 sigfigs, or 31556000 or 3.1556x10^7

• Anonymous

60sec x 60 mins = 3600 sec/hour

3600sec x 24hours = 86400 seconds in a day

86400sec x 365.24days = 31556736 seconds

Since the question has numbers with 2 sigificant figures in it (60, 60, 24), we have to put our answer into 2 significant figures, which would be:

3.2 x 10^7 seconds, or 32000000 seconds.

60sec 60min 24hrs 365.24days =60*60*24*365.24=

1min 1hour 1day 1year

=31556736 seconds/year

The number you had is correct from your information. Now if we are dealing with significant figures we look at the least significant figures since we are dealing with multiplication. Therefore there is only 1 significant figure.

Final answer= 30,000,000 seconds/year or 3*10^7seconds/year