everybody write down Admiral abbar because what we're doing today it's a trap whenever you see mixed operations on an exam be forewarned the test bank is trying to trick you when you do a mixed operation problem you have to follow the order of operations and keep track of your signific figures along the way for example we have addition in parentheses here so we're going to do addition first and you're saying Dr Kelly why is this a trick we know order of operations we've been doing order of operations since we were a little kid what is the trick here well here's the trick I'm having trouble resizing here give me just a second here oh no if we looked at this problem we have three sigfigs in this number four sigfigs in this number two sigfigs here two sigfigs here and on a multiple choice exam I guarantee you the very first answer will have two sig figs why is the answer not to Sig figes because of your addition they will always try to trick you when you perform a mixed operation calculation into guessing an incorrect number of sig figs do your addition step like you're supposed to 9.6 * 10 7th plus 7.4 time 10 the 6 you have to go to the higher power again right go to the higher power that's 9.6 time 10 the 7th move that to the 7th as well the last place value they have in common is right there so our answer winds up being 10. 3 * 10 7th or 1.03 * 10 8th but either way we're coming out with 3 sigfigs now another thing that's important about mixed operation is is we're taking our answers and doing more calculations with them so we do not want to round as until the end and therefore I'm going to carry that insignificant four throughout my calculations so I'm going to use that subscript notation that I've been using so instead of having two numbers with two sigfigs here what I really have is one number that has three significant figures so when I begin my multiplication division step I've got three sigfigs three sigfigs and four sigfigs So my answer coming out of multiplication and division should have three significant figures so let's execute 3.45 * 1.03 or second e 8 divide by 8.3 48 second E3 and that gives us 4 2 7 3 2 3 09 nine out we should only have three sigfigs one two three so 4 27 round on the basis of that three better yet put it in scientific notation 4.27 * 10 to the 1 2 3 4 fourth so that's the answer you should give on an exam and that's why these are a trap write down Endor pause me right here and try this one yourself before I spoil your fun all right you're back do you have your answers ready let's take a look 3244 time 10 to the 8 minus 1.0 * 10 3r not to the same Power by any stretch 3244 go to the higher power that's going to be one two three four five so we're going to need four zeros so we're going to wind up with a number that has four significant figures coming out why because that's why because that's the last place value they have in common so even though it looks like we should have two sigfigs and matter of fact again multiple choice exam the first answer would have two sigfigs we actually have four sigfigs coming out of here so instead of having a number with two sigfigs there we actually have an answer that is four sigfigs isn't math fun math is so awesome nearly as awesome as the Death Star which you are now going to write down punch that into our c calculators the rest of the way and our calculator gives us clear myself some working room our calculator gives us 5 67074 439 how many sigfigs should we have we have four sigfigs here we have four sigfigs here and we have three sigfigs here so our answer should be three one two three we have a seven for our rounding purposes right there so we're going to round our six up so 570 Z scientific notation always works best one 2 3 4 and there is our answer chemistry is easy life is hard join me for get another exciting lecture in a few minutes