all right we are in concept three of unit one which is dimensional analysis and scientific notation so these are two more I call them math skills that you really need to know and understand as we move forward into all of the other content we're going to learn this year so again this is just kind of foundational stuff that we need to know so you've already learned temperature conversions and metric conversions and if you did my long way with metric conversions dimensional analysis is is going to be so easy um but if you've been taking shortcuts on it now it's going to be harder so hopefully you did it the long way the first time and we'll see how it goes so dimensional analysis the purpose of this is it's just a technique and we're going to use it to convert numbers into different units without changing their value so you did this with metric conversions changing kilograms to milligrams you just using a different ver uh versions but you were working within the same family you were in the group grams family or the meter family going from centimeters to meters here we're going to change families so we can jump from liters to cups or Pounds to milligrams that kind of thing so this is really really useful when you're baking or cooking um you'll have to do this a lot like if you lose your tablespoon but you have a teaspoon you can figure out how many you need of each also traveling to foreign countries that use different units from us um like in the airport you know you can't have a bag more than 50 pounds but when you're in Europe how many kilograms is that so you'd be able to do these types of conversions also really important for building or engineering so if that's a field you're interested in this is something you would need to be able to do we accomplish this by multiplying given numbers by conversion factors in order to get our number into desired units and I've been mentioning conversion factors in the metric conversion notes and the measurement notes we just took um but now let's get a definition in our notes they are ratio of equivalent values meaning they equal one that's why we're able to use them to convert units without changing the value of the measurement so we use them indenial analysis when we want to alter the number again without changing its value so an example of a conversion factor how many hours are in a day well most of us know there are 24 hours in one day I can use that as a conversion factor so I can write it as 24 hours divided by one day or 1 day divided by 24 hours either way you do this that equals one which is why I'm able to use it as a conversion factor so both of these format could be useful another example 12 in is a foot most of us know that so you could write that as 12 in divided 1 foot or 1 foot divided 12 in because both ways that conversion factor equals one so you try what would be the conversion factor for days in a week good job seven days equals one week or seven days over one week or one week over seven days all right so the steps to apply this into a real problem that you would get are exactly like the metric conversion steps so that is awesome you write down the given number and unit draw your picket fence use the chart to fill in appropriate conversion factors making sure they're on opposite sides of the fence to cancel out multiply across the top and then bottom and then divide so let's start off with one that you probably know these conversion factors in your head already how many seconds are in one year so first what do we know we know one year step two draw your picket fence all right step three I don't know how many seconds are in a year but I do know that there's 365 days usually if it's not a leap year in a year so one year is 365 days now why did I put it this way instead of the opposite well I want the year unit opposite of each other all right now I don't know how many seconds are in a day but I know that there are 24 hours in one day and then I know that there are 60 Minutes in 1 hour and then I also know that there's 60 seconds in 1 minute again I'm C putting the like units opposite so they will cross out so all I'm left with is what I'm looking for then I multiply across the top so 1 * 365 * 24 * 60 * 60 and then 1 1 * 1 * 1 that's nice and easy and then I divide and that's how you get your final answer right another example how many feet are in 250. 4 cm well first write the given unit and or number and unit which is 2504 cenm step two draw your picket fence step three fill in appropriate conversion factors again I don't know how many centimeters in a foot but on the chart that I will give you of conversion factors it will tell you there's 2.54 cm in 1 in so I can use that and then I know that there's 12 in in 1 foot I multiply across the top multiply across the bottom and then divide and that's how you get your answer so 254 50.4 cm is the same as 8.22 ft all right so these are the conversion factors I will give you so you will always have these to use on an assessment you do not need to memorize these you just need to know how to work with them all right so use this and I want you to do this next slide all right so I want you to pause and I want you to do these conversions I know I could just skip through and give you the answers which I'm going to do but I really want you to pause and do this so that you know what you're doing and then when you're ready here are your answers all right the last math skill we need to practice is scientific notation so the purpose of this is we're going to rewrite really large or really small numbers into a format that just makes it easier to use and see and work with and that format is just the digits with a decimal point after the first digit followed by time 10 to the power which represents how many places the decimal is moved so that is a lot of words for something that's a lot simpler if you just look at it so for example 50,500 is kind of a decently large number it's not that big but I would write it as the first digit which is five and then a decimal point with the other digits time 10 4th because to get this decimal here from here I had to move it four times 1 2 3 4 to get it there we will write out these steps don't worry but this is just what I mean by The Format of what it's going to look like it's always going to be a digit and then the decimal point so here are the steps first move the decimal so that there's only one digit in front to the left of it then you're going to rewrite the number as that digit decimal and then any other digits that are there if there's no other digits you just put a zero and then put times 10 after it then you need to add an exponent right here to represent the number of places that you move that decimal in step one so did you move it three times four twice once what' you do now for that exponent you need to determine if it should be positive or negative the easiest way that I remember this is positive if you started with a big number so a number greater than one so like when we had 50,500 that's a big number so it was positive exponent or it's negative if you start with a small number so a number less than one like 023 I would use a negative exponent when putting that into scientific notation I think if we do some examples this will make way more sense so let's put it into practice all right convert 100 101,000 into scientific notation all right so this is where my decimal is when it's not written in it's right here but I want it to be right here all right so that's where it is now that's where I want it to be count how many times you're going to have to move it to get it there all right so to get it there because that's where I want it right there I'm going to have to move it five times all right one 2 3 four five that's how many times I didn't you move it now this is positive because it was a large number to start with that's how I knew that that was positive all right so that is your final answer 1.01 * 10 5th all right example number six convert 0.0098 into scientific notation so first here's my decimal I want it to be here in scientific notation so I want it to be 9.8 time 10 to however many times I move it so if I'm G to move that decimal I'm gonna have to move one two three times now it's going to be a -3 because this is a small number this is a number less than one that I'm starting with so that's why I'm going to make it negative exponent that's your final answer all right now the only other way you would see this is we can go the other direction so we can go to standard notation which would be to take it out of scientific notation and just make it a normal number so this is honestly even easier so when I'm looking at this all I need to do is look right here this is just going to tell you how many times you need move the decimal so I'm going to move the decimal twice now because it's positive I'm going to make this a bigger number so I'm going to move the decimal this way to make it bigger all right so two means I'm going to move the decimal twice positive means I'm G to make it bigger so I'm goingon to move it one two times and then I just rewrite it 25.7 all right let's try another convert 3.1 * 10 the4 into standard notation so we're just taking it out of scientific notation so I'm I'm going to move it four times and negative means I'm going to make this a smaller number so this time I'm going to go this way so 1 2 3 four that's where my new decimal is going to go now what goes here you just fill those in with zeros and then rewrite 0.0031 all right now if you feel better going One Direction versus the other you can always double check so move this back and see if you can get it back into the scientific notation you started with all right pause the video now and try these and there are your answers to know if you did it right and now we're going to practice this so much in class so that you are scientific notation chance