# Thread: Significant Figures and Rounding

1. ## Significant Figures and Rounding

Hello,
Recently I have encountered a problem in which I was to figure out how many seconds I was in class each week. My class is 0.833 hours long and we meet three times a week. I came up with 8,996.4 seconds. I need to round this to three significant figures because there are 3 in the information provided in the question (correct?) but everything rounds up and I would have 9,000...which is not 3 significant figures. Help please?

2. ## Re: Significant Figures and Rounding

Originally Posted by Phillipians314
Hello,
Recently I have encountered a problem in which I was to figure out how many seconds I was in class each week. My class is 0.833 hours long and we meet three times a week. I came up with 8,996.4 seconds. I need to round this to three significant figures because there are 3 in the information provided in the question (correct?) but everything rounds up and I would have 9,000...which is not 3 significant figures. Help please?
Round you answer to 9000 and then give it as $\displaystyle 9.00 \times 10^3$

3. ## Re: Significant Figures and Rounding

Hello, Phillipians314!

Recently I have encountered a problem in which
I was to figure out how many seconds I was in class each week.
My class is 0.833 hours long ?? and we meet three times a week.
I came up with 8,996.4 seconds.
I need to round this to three significant figures
because there are 3 in the information provided in the question (correct?).
But everything rounds up and I would have 9,000 ... which is not 3 significant figures.

First of all, why did you write the length of your class as a fraction of an hour?
. . And then try to convert hours into seconds?

If your class is 50 minutes long,
. . then it is: .$\displaystyle 50 \times 60 \,=\,3000$ seconds per meeting.

With three meetings per week,
. . you spend: $\displaystyle 3 \times 3000 \,=\,9000$ seconds per week.

The answer is accurate to three significant figures: .9000

4. ## Re: Significant Figures and Rounding

Originally Posted by Soroban
Hello, Phillipians314!

First of all, why did you write the length of your class as a fraction of an hour?
. . And then try to convert hours into seconds?

If your class is 50 minutes long,
. . then it is: .$\displaystyle 50 \times 60 \,=\,3000$ seconds per meeting.

With three meetings per week,
. . you spend: $\displaystyle 3 \times 3000 \,=\,9000$ seconds per week.

The answer is accurate to three significant figures: .9000
I have to disagree with your answer, Soroban. Trailing zeroes are never significant unless they come after a decimal point.

5. ## Re: Significant Figures and Rounding

I'm going to jump into this and say that the number of significant figures is ambiguous for "0"s. I won't say, like mr fantastic, that "trailing zeros are never significant" (emphasis mine) but certainly you need to write $\displaystyle 9.000 \times 10^3$ in order that the number of significant figures not be ambiguous.