Whenever you perform these operations while using sig figs, your final answer should have the same number of sig figs as the number with the LEAST number of sig figs. So, let's take the third one for example.\[485.369\div0.124=3914.26612903225806\]Now, let's see how many sig figs we should be using. For 485.369, this number has 6 sig figs. For 0.124, this number has 3 sig figs. So, since 3 < 6, our final answer should have 3 sig figs. Rounding our answer, it will be 3.91E3 (notice how scientific notation makes this nice and neat for sig figs.
wait now im even more confused. . .
Which part has you confused?
First of all, do you see how 485.369 has 6 sig figs?
yeah i get that part. i dont understand what the e is for
E is a shortcut for scientific notation. So, \(3.91E3 = 3.91\times10^3\) (Sorry for being ambiguous, I should've made that more clear.)
oh ok lol . so let me try another one on my own but dont leave just incase i dont get it pleasee
for A being that theres 2 significant figures on both sides does that mean the answer has 2?
Wait, one more thing, I forgot to mention. The rule ^ works for multiplication and division. Addition and subtraction is slightly different. For addition and subtraction, you use the number of decimal places of the LEAST amount of accuracy. So, for example, if we had: \[0.123 + 0.00132 = 0.12432\]However, 0.123 has the least number of decimal places, so your answer will be rounded to 3 decimal places. So, we would get 0.124.
So, for A, after you add them, your answer should have 1 number to the right of the decimal because 1.2 has the least precision.
oh ok so would that answer be 1.3 e3?
The 1.3 would be fine. You wouldn't need the e3 because the number isn't bigger than that. The reason I used the e3 before is because my answer to that first example would've been 3910 (compared to the original of 3914.266). 391 are DEFINITELY significant figures, but the 0 is in a bit of a gray area. So, to make sure that it's clear that we mean for 3 sig figs, we use scientific notation and say 3.91 e3. The 3.91 part shows that you meant to have 3 sig figs, and the e3 (or \(10^3\)) makes clear what your actual number is because 3\(3.91 \times 10^3 = 3190\), as we intended.
Ignore the 3 before the \(3.91\times 10^3\) at the end.
oh ok let me try one more?
b would be 0.1 right?
Hmm, not quite. You're multiplying here, not adding, so your answer should have the same number of sig figs as the number with the \(least\) sig figs.
So, when adding and subtracting, you deal with decimal places. When multiplying and dividing, you deal with sig figs.
Maybe this will help? http://chemed.chem.purdue.edu/genchem/topicreview/bp/ch1/sigfigs.html
it would be 0.16 ?
Yes! Good job! Just to make sure you had the correct thought process, you got 0.156 in the original, both 1.2 and 0.13 had 2 sig figs, so your final answer will have 2 sig figs. 0.156 rounds to 0.16 when you have 2 sig figs.
Ok thank you so much :)