Significant Figures?

Question

(8.2156 * 10^2) *(3.12)

what is the answer? round to the significant figures

this is not a simple algebra question i know it 2563.2672 is the answer 256 * 10^1

please explain our answer

also what is the significant figure for (6.042/7)

is it 1 or .9 or 0.9

Answer 1

0.9 and .9 are the same thing -- zeros to the left of the decimal point, without any other numbers in front of them, don't matter, because they can always be done away with by rewriting in scientific notation.  

Bearing that in mind (and the answer is 0.86314), don't round to the next place value (here, you're trying to go from tenths to ones).  Use the tenths place value, since that's the greatest one with any digits that count in it, and round to that.  So it's 0.9, or .9.  

For the first one, you could've just as easily answered "2560" -- but not "2560."  The second one means the 0 is a significant figure, but in this case, you're looking for 3 sig figs, so use the first one (or rewrite it in scientific notation, which would usually be 2.56 x 10^3).  And, you're looking for 3 sig figs because that's the least number of sig figs you have in your data that you start with: 8.2156 has 5 sig figs, but 3.12 only has 3 sig figs.  So your answer is only sure to 3 sig figs.

And do look at that link the other person gave: it does have a good explanation.

Answer 2

check out http://www.chem.tamu.edu/class/fyp/mathr... about half way down the page.  Explains sig figs well.