next topic is how your calculators can lie to you that's right what you have been telling your algebra teachers all these years is 100% correct your calculators do lie what do I mean by that let's take a look at a really simple example I have here my square and my square is 2.4 CM by 2 4 cm and I want to know what the area of my square is well area is length times width so my area is 2.4 CM times 2.4 CM punch that into my calculator and my calculator is going to give me 5.76 cim squared turns out my calculator is also running for political office this year because it is lying to me how is it lying to me some of you are saying well I did this by hand and I got 5.76 to here's the problem when we took a measurement here we only had two significant figures we were only capable of measuring two numbers but suddenly our calculator is telling us we could measure three not only that but our measuring tool it only let us measure to the T place and all of a on our answer is supposed to go to the hundreds something isn't right here mathematical operations can create numbers that do not represent things we were capable of measuring in the laboratory therefore whenever we do a mathematical operation we have to apply what are known as significant figure calculation rules for multiplication and division that rule is very simple the product has the same number of significant figures as the least number of the numbers multiplied now it's one of those things that easier for me to do than it is to say if we come up here to our example I had two numbers in I had two significant figures in this measurement I had two significant figures in this measurement therefore my answer can have no more than two significant figures so this number right here should only be two sig figs so one two and I am going to round on the basis of the six I'm going to round away that six so my 5.7 six becomes 5.8 cim squared and that would be the answer I would report in a scientific journal or that would be the answer that I would type up and give to my boss now whenever you round a measurement and then do a calculation with it you create a phenomenon known as propagation of error so if you're wanting to keep track of an insignificant ific figure so that you can use it in further calculations you can use this notation technique and you'll see me do it all the time where I would write my answer as 5.7 and then I would write six as a subscript that way I know that this is significant and this is significant and this is an insignificant number carried forward for calculation in the computer program where you do your homework this is the answer that you would whoops that stop all right this is the number that you would put into the homework program this is how I'll often write my answers when I'm doing a demonstration or when I'm doing further calculations and I'll remind you of that notation it's also standard notation technique that you're going to see chemists and physicists in particular using constantly so you need to be aware of it because if you're in this class you're going to be dealing with chemists physicists and biologists let's look at a couple really quick examples first and foremost let's take a look at an easy one I have 7,212 multiplied by 1.4 my answer should have how many significant figures well this measurement has four significant figures this measurement has two significant figures So my answer should have two significant figures because my answer is going to have the same number of significant figures as the smallest number in my measurements so let's punch that into our calculators my calculator gives me this answer I'm going to come over here and I'm going to say I've got two sigfigs one two so those are my two sig figs I round on the basis of that place value and that place value only you have to preserve place value this place value can't be changed that zero there has to be in the same place value so I have to do one of two things I either have to write this as my answer in which case I've really confused the number of sigfigs because I had to ambiguous zeros when we know that this zero is significant and all of these are insignificant so what can we do to clarify we can use scientific notation so the way we should really write this answer and the best way to write this answer would be 1.0 time 10 to the 1 2 3 4 time 10 to the 4th Newton meters all right I should tell you to write down the best football team of all time the Tennessee tit there is only one right answer to that question I must be very insistent all right let's take a look at another example here let's multiply these two numbers first how many significant figures in each I have four significant figures here here I have three significant figures zero is at the end of a number without a decimal or ambiguous and when push comes to sub shove we say no they are not significant for purposes of calculation so our least number of significant figures is three we're going to say three for our answer despite what I to spent 20 minutes telling you a couple lectures ago for multiplication division addition subtraction when push comes to shove we count ambiguous zeros as insignificant so we punch this into our calculators and that's our calculator selling swamp land and Florida we have to have three sigfigs one 2 3 round on the basis of that place value and that place value only so we have 4 09 0 0 0 again this is the perfect example of when scientific notation would be ideal 1 2 2 3 4 5 so 4.09 * 10 to the 5th met squared chemistry is easy life is hard yes um scientific notation doesn't really change things if you have not watched my video on how to put scientific notation into your calculator pause what you were doing and go do it now if you have not watched my video on how to put scientific notation into your calculators stop what you're doing and go do it now we have three sig figs here three sig figs here the fact that we're in scientific notation isn't going to change the fact that our answer should also have three significant figures so we have 2.97 second e 4 times 4.56 2 e E3 equals 1.35 432 * 10 8 met squared now if your calculator doesn't default to scientific notation I've got a video for that too but you may have also gotten 1 three five 4 3 2 out of your calculator either way it's your calculator line not just lies damn lies oh everybody write down MGM everybody write down MGM we have to have three sig figs so these are our three sig figs we're going to round on the basis of that four and that four alone oh you know what I did by the way let's go real quickly to um this one up here I didn't round cor correctly did I on this one we've got two oh I did round correctly up there I'm fine I'm awesome I'm awesome sauce okay back to this one round on the basis of that four and that four alone 1.35 time 10 to the 8 m/s two more examples I want you to write down the Bengals write down Bengals I want you to punch this problem into your calculator before I do the answer so pause me real quickly put this into your calculator all right are you back with me I hope so 1 Point 879 seconde E4 divided by 1.82 E8 you should have gotten from your calculator the following lie 1.43 and then lots of eights basically repeating eight times 10 12 if you did not get that answer out if you did not get 10 to 12 as your answer you put it into your calculator wrong go watch my video make sure you're doing it right to put it into your calculator you should be going 1. 1879 using that e button four divide by 1 eight using that e button negative 8 and then hitting the equal sign if you're not getting this out Try It My Way notice when you use the E the e e button you don't use your power of you don't hit times 10 karat right that e button does it for you and drops parentheses watch the video people significant figures which is the topic of this video two significant figures here four here so our answer should have two one two so 1.0 * 10 to the 12 m per second let's do um one more quick example and that's this one right here again pause me and try to get it on your own I hope everybody paused me like I asked and you should have gotten 8.8 repeating times 10 to the 17 well you've got two sigfigs here two sigfigs here so your answer should be 8.9 * 10 to the 17th m/s I am very concerned that you should have gotten that 17th if you don't believe me remember your rules for math class let's take a quick look look for a algebra moment of the day remember remember True Believers 10 x * 10 Y is 10 to the X + Y and 10 x / 10 Y is equal to the 10 to the x minus y just a little refresher there we'll be dealing Lots with those powers of 10 later that's it for this lecture see you on the flip side