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Scientific notation test this is the multiple choice section of your test it is worth 100 points form

today's lesson how to do scientific notation on your calculator this is one of the most frustrating things in the world for me to teach because frankly no one listens to me and people get things wrong all the time because they don't know how to use scientific notation on their calculator they do it their own way and they get it wrong so how do you put a number in introducing the e button locate that button on your calculator oh what's that you don't have a calculator well I told you to bring a calculator every day not my problem you should really have one if you don't have one go buy one you should have your own calculator every day because different calculators are going to look different you're not you're going to learn how to use one calculator then you're going to steal some of the other calculating you want how to know how to use it it's really important that you learn how to do this on your calculator and always have that same calculator because I did not wish to teach you in the middle of a test how to use your calculator I'm doing that now I'd rather not do this again so the e button the e button is going to look like one of these three things it's silly they're going to look like a double e as in this old TI model the e e button the scientific notation button is right here for that one for Casio what you generally shows up on the bottom and it looks like an exp right here or we have a lot of you're familiar with this one this is the one that the math department uses it's this button right here this I can't get it to focus but right here this time is 10 to the in button right there so please locate that on your calculator that's what it is that's where to find it if you can't find it I'm going to you'll probably pause the video here make sure everyone in the room has found that button on their calculator those are all different labels but they all do exactly the same thing it takes the number that you just didn't put it and then put it and then it puts in a times 10 whether it shows it or not it puts it in and and then it waits for your exponent it waits for your exponent so if I have for example three point zero seven times ten to the fourth and I want to put that into my calculator I'm going to hit three point zero seven I am NOT going to hit x I'm not I'm just going to hit my e button put it in scientific notation the three point oh seven and now I'm saying hey I want this in scientific notation calculator so I just hit the scientific notation button and different calculators show it differently this calculator puts a capital letter E there other calculators if I were to use the math calculator I hit three point zero seven and whenever I hit this times ten to the button it comes up times ten to the so it's pretty obvious that they put that ten in there and it's waiting for that exponent and on the old key is the EES over here it's going to look like three point zero seven and then my EE button here and on this particular calculator shows doesn't show the ten at all it just shows the exponent you can tell that I'm waiting for the exponent so if I had a four now it shows up as the exponent but a four here comes after the e if I had a four here comes up as an exponent now if you have this particular calculator a lot of times it's confusing how to get out of exponent mode on this one you just hit the right button and that gets you back down into regular mode so different calculators different ways of getting there and they'll all look different but those are all the same numbers those are all thirty thousand seven hundred written in scientific notation so make sure that you know what that looks like on your calculator similarly when you get a number out when you do a calculation and it shows the answer it's going to show it in this format if you have this calculator it's not going to say x ten you need to know that's times 10 to the fourth when it puts that little exponent up there and for this calculator if you ever see a capital e that means it's in scientific notation and so if I hit equals on all these it will give me a decimal answer as long as it fits on the screen these will just this will spit out decimal answers when you hit equal so so now let's see there are other ways people can put these in but they involve knowing what you are doing and I don't trust that that's the best way to teach you how to do it so let's say that I want to divide two numbers I want to divide 3.07 times 10 to the fourth divided by six point two times 10 to the negative third and I want to know what that number is well for the Casio model and the TI model these are actually both very easy things to do you can just put the first number in 3.07 times 10 to the fourth 3.07 times 10 to the fourth by the way some models of the TI you have to actually hit the second function to get to the e e to get to the scientific notation I find that annoying but anyhow you have that now you hit divided by six point two times 10 to the negative third do that over here divided by six point two times 10 to the negative third and I hit equal on both of those and I get the same number that's good that's good got the same number notice that I didn't put in parenthesis probably should have but on these calculators when you're in scientific notation it knows that you're in scientific notation and it groups those together like you're thinking however with the math department calculator this is not the case that are very particular about orders of operation on here so if we put that same number in 3.0 seven times 10 to the fourth divided by six point two times 10 to the negative third this is not going to give you the same answer notice that our number back here was in the 1-1 dude like 4.9 million yeah it's in almost 5 million whereas this number is almost 5 so we got a difference of about a factor of a million and this calculator did the right thing in this calculated the right thing they're just kind of programmed to handle these numbers in different ways this one uses the strict mathematical interpretation that we are just because you didn't put any parentheses in there lets the difference is that this automatically groups scientific notation numbers that kind of puts the parentheses in here when you use scientific notation and this one doesn't if you do the same calculation without parentheses notice that we're taking three point zero seven we're then multiplying it by 10 to the fourth we're then dividing it by six point two and then we're taking that answer and taking it times 10 to the negative third and that's a different answer than if we divide by that whole group you're going to get a significantly different answer so if you have this calculator you better make sure to always use parentheses I know your math teachers say to always use your parentheses and that's not bad advice it's just that these other calculators are smart enough with grouping scientific notation numbers that you don't have to although it never hurts to put them in parentheses so go ahead and do a few divided by now this matters in dividing it's when you're dividing and you're dividing scientific notation numbers you either got to have kind of calculator that can handle it easily or you've got to make sure to always put your parentheses in and that's something that is going to come up a lot so you better learn how to do it