[achibaby1974]

1.)

7.967e-4 + 8.0e-4 = .0015967

My prof said we should count the digits trailing the decimal point.
WHY? What does that tell me? The number of sig figs maybe? That's the only thing that seems logical. Ok. So then:

7.967e-4 -------- goes up to -7 so 7 sig figs?
Then 8.0e-4 --------- goes up to -5 so 5 sig figs.



So what is my answer? Why do I have to count all that? What is that telling me?

Because, isn't the rule for +/- to fewest number of places after the decimal? In that case, 8.0 is the one with the least amount of places after the decimal. It has only one. So my answer .0015967 would be 1.6e-3.

OR

Do I use the counting rule thing to go to the least places after the decimal. In this case this would be.. the -5? So, would my answer be 1.5967e-3 OR would my answer be 1.60e-3 in that I count that it goes up to -5.


OKAY now a kinda tricky one.


2.)

(9.827e-5  +  3.54 e -6) / (2.7651e-3  -  5.1e-6) = (.00010181) / (0.00276) =                              (1.0181e-4) / (2.7600e-3) =  0.036887681

ok. when +/- use the least decimal places right? So for the top half they're both 8? So it's 8? The bottom half are both 7. So it's 7? Then when we divide that's 8 sigfig over 7 sigfig so we use 7? So that's 3.68877e-2.


or

when dividing we just use the sig figs provided, not counting afterwards? 1.0181e-4 has 5 sig fig. 2.7600e-3 has 5 sig fig too. So that would say that the answer would need 5 sig fig. So Then the answer would be 3.6888e-2.

See what I mean? It's very confusing!!!!      

[Arkcon]

1.)

7.967e-4 + 8.0e-4 = .0015967

You've done a good thing by using scientific notation for the left hand side, now do the same for the right hand side as well.

[EDIT]
When adding and subtracting, you keep the same number of decimal places as the number with the worst precision.  Pretend you got those first two numbers by weighing on a balance scale.  You don't know what is in the third decimal place of the second number, so you can't use the third decimal place in your final answer.

Sig figs were a long time ago for me.  Lots of different places have slightly different rules.