Question

Does anyone know the significant figures of these?

Answer 1

When you multiply it is easy to tell (especially in scientific notation like you're given in these problems). All you need to do is look at the LEAST ACCURATE number. (i.e. the number with the fewest number of sig figs.)
In the first question, we have 7.05 which has 3 sig figs (0 is included because it is surrounded by non-zero numbers) and 3.65 which also has 3 sig figs. We can ignore the 10^-6 and10^-4 because all of the zeros added by those will be place-holders to get out to where the value is (hence why scientific notation is nice. It takes all the non-significant figures and makes them disappear in the handy 10^n)

Addition I personally find a little bit more tricky...

Answer 2

When you add or subtract measurements, they can contain no more decimal places than the LEAST ACCURATE number (you'll notice that when talking about sig figs, we always reduce to the least accurate number.) In this case it is probably worthwhile to expand the notation, so we have \[0.00000705 + 0.000385\]We can see from this that we should have 6 sig figs since there are six decimal places in the number with fewer decimals.

HOWEVER
I would also note that I am not positive about this one...my guy says it should be 3 sig figs. Usually the addition rule has to do with numbers like 1.0045 + 2.3 => 2 sig figs. Since I'm used to dealing with units of the measurement as well, if I had two numbers like that I would probably express them as micrometers or something of the sort and so have 0.705um + 38.5um => 3 sig figs.

Answer 3

Hope that helped a little. (also, it is probably more common to refer to the least *precise* number and not least *accurate*. If you don't really understand the difference between precision and accuracy I can try and explain. Or if it confuses you too much don't worry about it too much right now.)