 There's the magic ding so we're live. It says this in previous math courses in theory We learned how to convert within and using the SI system and the imperial system of measurements now I got to be honest. I've always found for me as a math nerd measurement was never my favorite topic now having said that I Do have to say to you. This is one of the few things you'll probably use some day almost everybody at least once in their life owns the house and decides to redo the kitchen or build the basement or do an addition very few people never swing a hammer or Use a saw or use a drill during their entire life So a lot of this measurement stuff is also just to give you kind of a context so that when you're trying to plan stuff out You know the vocabulary which helps so I would argue it's useful in some ways It says you learned how to convert between the SI system and the imperial system of measurements Canada went metric when I was in grade one in 1976. I believe it was we went metric Pretty much every country except the US has gone metric The imperial system is feet inches pounds, which we still use in our metric society I'm willing to bet most of you don't know your weight and kilos Most of you probably don't know your height and centimeters. Most of you do weight and height in pounds and feet inches there enough You got three methods last year Method one was using the SI chart as a number line Method two was called proportional reasoning and method method three was unit analysis It says in this lesson, we will do a basic review of these methods and also introduce the concepts of accuracy Let's all underline the word accuracy if you're planning on buying the book if not you're gonna be copying these notes out on a separate piece of paper and Precision in measurement says recall the following charts used for conversion It's a little interesting actually as it turns out because a lot of these prefixes weren't important when I was young Computer memory and technology has made some of these prefixes become more and more important For example, most of you if you want a thumb drive, it's in the gigabyte range. I Can remember my first computer hard drive. It was eight megabytes and I was wondering how will I feel that? Eight megabytes a song and a half if you're putting it into mp3's basic basically, but seemed like wow, I'll never feel that I Just bought a new computer two weeks ago the hard drive. What comes after giga? I got a terabyte hard drive and I thought to myself. I'll never feel that two years from now I'm sure it'll be full so we have our metric prefixes The other one that's becoming more and more important in your society is nano When I was in high school, nobody knew the word nano technology More and more stuff is becoming so small. It's becoming Available on the nano size You can think of these as being on a metric number line it says I Really don't like the way they've written this as decimals. This is one time I think powers of 10 are much much handier So here's what we're going to do if you are planning on writing in your book. Take your pencil out giga. This is actually 10 to the ninth Write that above the 10 it is there's nine zeros Mega is 10 to the sixth I would rather use the exponents because typing nine zeros a I'm likely to make a mistake and miscount and it's too much typing Kilo is 10 to the third Hecto lowercase h is 10 to the second and Deca is 10 to the one Tasha You're in elbow. Okay, write this down or Offer to stick around and do the whole lesson after school So you got your workbook if you're planning on buying it start writing my child Shayan by the way, I know there's a one there. I'm not gonna write the one where because that's too much work Let's go over this way You remember from your scientific notation lessons way back in science 10 How do we do decimals in scientific notation David? this is gonna be 10 to the 1 to to the negative 9 and Micro Now micro by the way has a weird symbol. We can't use M because M got taken by Millie Micro the symbol is actually where our letter M comes from. It's a Greek letter. It's a Greek letter mu or the Greek cat say mu Yes, it's a math joke. It's 10 to the negative 6 Millie is 10 to the negative 3 Santy is 10 to the negative 2 and desi is 10 to the negative 1 Then you have what we call your base units meters grams leaders amps Candles, those are physics units. I'm pulling up jewels. Thank you Bolts So this is 10 to the 0 which really means no 10s By the way, what's anything to the 0 power who remembers their exponents not 0 it's 1 1 okay So each movement of one position it says represents the power of 10 and Since it represents the power of 10, I find it easier to have the powers of 10 there in front of me Then last year I think on your provincial you're given a conversion chart Feet to inches inches to centimeters centimeters to inch it whatever blah blah blah blah blah It says more conversions can be found online heck there's an app for that turn the page or Next page over page 2 Says this in the metric system the units are related to each Each other by factors of 10 from the metric unit chart. We can create a metric unit number line for use in conversions Blah blah blah, you know what? Let's just jump and let's do an example Example one says this use the metric unit line to complete the following One meters one meters one meter to centimeters One meter is how many centimeters? hundred now prove it By the way, I'm glad they started with this one because we know what the answer is What if I didn't know how to calculate the answer? Here's the method that will always work and Zach if you do these intuitively in your head great I'm not gonna make you show me work But I will this time for the one that we know the answer to let's write down a method that always works First of all, we're starting out with one meter write that down in B. The first thing that we would write down would be 2.3 in C the first thing that I would write down would be 750 and then because they're prefixes Because these are powers of ten. I always write down a times ten to the and then this method will always work What was the power of ten that we associated with meters ten to the what? Go look on the chart as a number, please Zero what was the power of ten we associated with centi? If you go as your exponent the first one minus the second exponent That will always work. It looks complicated, but actually it's the first one minus the second one now I have a minus minus here. What's a minus minus to Mara the same as really? This is the same as get my calculator out one times Ten to the power of what zero minus minus two there's the one hundred that you all just know Where it comes from you can turn it into an equation Do you have to know is it worth learning this? Hey, you won't be able to do every one of these in your head This is the method. This is my fallback method Chelsea if I don't know what to do gives me 100 let's try B 2.3 liters to milliliters So what I would do is I would go times by ten to the what was the prefix for? What? Get a question. You have a question. Oh, okay What was leaders? Zero minus what was Millie negative three This is going to simplify to This is our base units. Is there a prefix at all in front? So when there was no prefix, what did I put in that column ten to the what? That's what the zero can't Honestly, I just remember no prefix. What's no as a number? It's going to be two point three times ten to the power of what is zero minus minus three 2300 by the way now's the time for you to figure out where the heck your exponent button is on your calculator if you haven't already 2300 Milliliters it is not the exp those that have an X. It's not that for most new calculators It's just a little hat symbol most of the time Note that'll just put a two on there that'll square it, but you need a generic exponent Why to the X is the other one that shows up. Yes So try typing two point three times press your exponent button Sorry two point three times ten then press your exponent button the third See so if I'm gonna do see and I want to go from centimeters to meters 700 centimeters now. I know it's seven point five, but what if it's not one I can do intuitively again? I would go like this Times ten to the what's the prefix? What's the power of ten that goes with senty? negative two minus Zero which what is negative two minus zero just plain old so I can go to my calculator and I type in 750 times ten to the power of negative two and that gives me the correct answer Again, Kayla, let me emphasize. Do you have to do it this way? No But will you be doing questions in your homework that you don't intuitively know the answer for yes However, if you've got a system that works for you Tasha all the time Good. I'm just trying to give you something that works. By the way, also, you'll notice a minimum amount of writing Also, I like it seven point five units meters Okay, Nicole we get to D. I'm willing to bet that D Most of you can't do in your head and don't just automatically see the answer. I don't No problem. I write down the number that they gave me seventy two thousand three hundred and fifty times ten to the Millie, what was the exponent of ten that went with that? Sorry negative three Minus Kilo, what was the exponent that went with that? You have the chart in front of you. I don't three So my exponent is going to be negative three Take away three It's not six So if I want to now I go to my calculator seventy two thousand three hundred and fifty times Ten to the power of negative six Negative button. Yep, probably does and I get seventy two thousand three hundred and fifty milligrams is point zero seven two three five kilograms zero seven two three five Kilograms Yep, you got the chart in front of you on the previous page Okay, you have to be open to this first of all Okay, no, it's not there. It's on the chart that we had in the previous page on page one Okay, so see Millie. What's the ten to the that we wrote? I told you to write above it negative three What's kilo minus and then what's kilo three? So it's always going to be your first one minus your second one always works I would answer did it give you a number in a fraction? Okay, I Will show you how yours so yours does fractions automatically you need to go from fractions to decimals Bear with me our calculators back to this so if You're looking for a standard procedure that will always work to convert with the metric prefixes Write down the number times ten to the whatever the first prefix is minus whatever the second prefix is and you get the power of ten from the chart Second topic is proportional reasoning. We call it cross multiplying often Says this in order to use proportional reasoning. We need to know one of the following a commonly known conversion or a ratio given in the question Let's go straight to example two says this Side show collectibles is considering making a statue of a dinosaur They are considering a scale whereby one centimeter represents 2.1 feet The height of the statue the dinosaur will be 12.5 centimeters. What's the actual height of the dinosaur? Okay To do this the key is to make sure you keep track of the appropriate units for each measurement And if you do that you can write one fraction equals one fraction and cross multiply I'll show you what I mean write this down pick your pencils right along with me The first measurement I see is one centimeter According to this sentence one centimeter represents what? So I'm gonna write 2.1, and I'm gonna put the word feet right there for a very good reason Equals I've just written a fraction a proportion and that fraction had centimeters on the top and feet on the bottom What I want to do now is write a second fraction a second proportion that has centimeters on top and feet on the bottom So I keep reading and it says this the height of the dinosaur will be 12.5 centimeters. I'm gonna say okay 12.5 Centimeters must go on top because that's what I had on top over here. I'll put an X there This is called proportional reasoning. It says look if you have two things and you know They're the same size write them as a fraction one over the other equals write your second fraction keep the units lined up and Hey, how do you solve one fraction equals one fraction? What was a shortcut you learn way back in grade eight cross multiply cross multiply If you know how to do it you don't have to write it down, but there was a deafening silence So I thought I'd write that down. How do we cross multiply? What's X gonna be? Well X times one is just plain old X X is gonna be 12.5 times 2.1 cross multiply says multiply diagonally So on your calculator What is 12.5 times 2.1? 26.25 units feet you can convert from measurements as long as you have a proportion as long as you write One fraction equals one fraction So example three says use proportional reasoning to convert point zero five miles to inches Huh? Well, let's go back and look at this chart here It would be great if one of these had miles to inches in it does it That's feet to inches that's yard to feet that miles to feet miles to yards inches to centimeters I don't see anywhere going from miles straight to inches What do I see we can go mile from miles to what I can go from miles to yards or to feet But I do notice Rashaun that I also have feet to inches I think it's gonna be smarter if I go from miles to feet take that answer Go from feet to inches. How am I gonna do that? Here's my first conversion factor I'm gonna write down One mile is the same as how many feet 5,000 what? 5,280 what measurement did they give me here point zero five Point zero five what? That's got to go on top then over I Can at least convert this to feet how many feet is point zero five miles I'm gonna cross multiply. It's gonna be one times x which is just plain old x. It's gonna be point zero five Times five thousand two hundred and eighty three hundred and sixty four two hundred and sixty four Two hundred and sixty four feet Right now we go from feet to inches now We could set up a fancy proportion here, but how do you go from feet to inches? What's the shortcut? Ah, we don't know How many inches are in one foot? Okay, so the shortcut is times by 12 if you don't know no problem. We set up another proportion One inch Sorry 12 inches is the same as one foot Let's find out and I got that straight from the first line of the chart right 12 inches is one foot I Feed on the bottom absolutely Rashawn since I used an x already. I don't want to get confused I'll pick a different cuz I asked you to I'll pick a different letter. Why cuz I asked you I know I'll just never get tired of that joke. I'm sorry. I Can't ever resist that. Why cuz I asked you to know Top audience Some of them just got it. Oh, okay Cross multiply again. We're gonna get y times one plain old y Equals 12 and Rashawn now we're answering your question. You were saying do we divide or multiply? What do we do multiply by 12 or divide by 12? It comes out of the equation. It looks like I'm gonna multiply by 12. Otherwise that 12 would be on the bottom here, wouldn't it? What is 12 times? 2604 3168 Is that correct people nodding and that's gonna be Interesting Turn the page We are going to Temporarily pause here Yeah, I'm gonna give you the take-home quiz today to work on I'm gonna give you a little bit of homework that we've done so far I'll give you the take-home quiz today because as I was speaking to you. I realized that for you guys. Am I talking? Thank you. I Realize that for you guys. This is a long weekend. You don't have school Friday So let's see if I can give you the quiz and get it done Wednesday and then no homework for the long weekend Now your homework from what we've done so far. However is if you turn, please to page six page six right now number one number two and Number three One two and three We'll do more when we finish off the lesson tomorrow, but now I'm gonna press stop and I'll give you your quizzes I just got to go forward to copy them really quickly so you can start on the homework of the quizzes back in about five