in this video I'm going to solve the Alex problem called interconversion of prefixed SI units there are three different versions of this problem I'm going to solve this version of the problem and I'm also going to talk about the other two as well in this version of the problem Alex is going to give you a measurement for a single object for me the object is a pill and the measurement is the pills Mass which is 900 milligrams you might be dealing with a different type of measurement like a volume measurement instead of a mass measurement Alex is asking me to calculate that measurement for a larger quantity of the same object so for me it's a hundred pills your different quantity may not be 100 it might be a thousand it might be 10 it might be 50. but it's going to ask you to recalculate the measurement in my case the mass for 100 objects and also it's going to ask you to report that new measurement in a different unit in my case it's be it's asking me to report it in kilograms so for this version of the problem there's two parts involved one is changing the quantity from one to a hundred and the other is changing the unit from milligram to kilogram for me now some versions of the problem only involve this part they only involve a unit conversion they don't give you any information about quantities at all because it's not necessary so one of the versions of the problem is just a straightforward simple well relatively straightforward and simple unit conversion let's start with just the unit conversion process so for me I am being asked to do a unit conversion from milligrams to kilograms from 900 milligrams into kilograms and if you are just starting out learning how to do conversions between prefixed SI units or between prefixed metric units whichever term you want to use if this process is relatively new to you then I suggest instead of converting directly from a prefixed unit to another prefixed unit that you instead convert from a prefixed unit to a non-prefixed unit in this case that just means stripping that Milli prefix away and converting from milligrams into grams and then converting into the desired prefixed unit it is an extra step but I will talk about why I suggest doing it this way as I set the problem up so let's go ahead and get started I'm going to start by writing the number and the unit that I'm working with and this I want to multiply by a conversion factor right now I'm focusing on doing I'm going to highlight it I'm focusing on doing my 900 milligram to gram conversion that's all that I'm thinking about so I want to get rid of the milligram units and to do that I'm going to set up a conversion factor in the form of a fraction that has my unwanted unit on the opposite side of where it starts originally so if my milligram unit is starting up on top we can kind of visualize this as being part of a fraction my milligram unit is starting out up top which means in my conversion factor I want that milligram unit to be down on the bottom and my desired unit which is grams because we're not thinking about this part yet my desired unit which is grams is going to go up on top and we'll look about we'll be able to see why I set it up this way in just a second now to fill in this conversion factor we've got to fill in these portions of the conversion factor we want to consult a table of metric prefixes or SI prefixes as Alex calls them Alex has a really good set of prefixes over in the data tab if you click on the data Tab and then open up SI prefixes it's a super comprehensive list it's giving you the symbols and the numerical meaning of each one of those prefixes right now we're dealing with the Milli prefix and we can see from this table that Milli represents 10 to the minus 3. so what that means the way that we fill that in here is that one Milli of anything it doesn't matter what it is is equal to 10 to the minus 3. 1 milligram is equal to 10 to the minus 3. now because I have it set up this way as you can see mathematically the milligram units cancel which is exactly what we want because we're trying initially we're trying to convert into grams so we have finished this step of the process we've successfully done this step of the conversion process and now we want to focus on this step right here so we're going to move on to the next step of the conversion process now we're trying to get rid of the gram unit the gram unit is located right here in our conversion factor we want it to be on the opposite side I don't know why I made that so big so we want if our gram is starting out on the top we want our gram unit to be on the bottom of the conversion factor our desired unit we want it up on top and to get the relationship or to be able to fill in the numbers here we're going to consult our table of prefixes here's kilo and we can see that kilo represents 10 to the 3 so that means one kilo is 10 to the 3 of whatever it is and the gram units cancel now let's before we do the math on this let's talk for a second about why I suggest doing this in two steps instead of just doing it all in one step these table of prefix these tables of prefixes give you the relationship between the prefixes and the base units the table of prefixes do not give you directly don't give you the relationship between one prefixed unit and another so if you wanted to go directly from milligrams into kilograms you would either have to look that conversion factor up somewhere else or you'd have to do that conversion factor in your head figure it out in your head if you have quite a bit of experience with doing metric to metric prefixes that may be really easy for you to do in your head it may be no big deal but when you're starting out initially this is the method that I suggest because it is less likely for you to mess this one up so let's go ahead and work the math out on this this is going to be 9 times 10 to the minus 6 and the units are kilograms and if you're stressing out about how did I get that number actually that's not even right 900 times 10 to the minus 6. so how did I get that number I just did the math on here 900 times 10 to the minus 3 divided by 10 to the 3. gives me 900 times 10 to the minus 6. so there I have done my milligram to kilogram conversion the last thing that Alex is asking me to do in this particular problem is figure out the quantity of a hundred pills not just a single pill so what I've done here is figured out the quantity of one or excuse me the mass of one pill one pill is 900 times 10 to the minus 6 Kilograms so I've calculated the mass of one pill in units of kilograms and now I need to calculate that for a hundred pills and to do that I'm just going to multiply by a hundred so if I multiply by a hundred both sides of this I'm going to have 100 pills and that mass is going to be 900 times 10 to the minus 4 kilograms now Alex is um uh let's see Alex wants this answer to be written as a decimal so one two three four point zero nine zero zero kilograms now let me talk really quick about the other two versions of this problem as I said before one version of the problem is not going to involve this quantity portion at all it's just going to be a unit conversion so you're just going to be doing this this step right here you're not going to have to do any of this kind of stuff the other version of the problem is basically the opposite of this so the other version of the problem is going to say something like 100 pills ways or has a mass of .09 kilograms and then it's going to ask you to go backwards what is the mass of one pill in say milligrams or some other unit skin is basically just asking you to do the opposite now you are going to if you have this version of the problem you're going to do the exact same thing you're going to start with your unit conversion you're going to start by converting if this was my problem I would start by converting 900 milligram 900 kilograms into milligrams so start by doing your unit conversion and then once you get the unit conversion in this step down here instead of multiplying to figure out the mass of a larger quantity you're going to divide to figure out the mass of a smaller quantity so if I had if I had this problem this type of problem in this step instead of multiplying by 100 I'd be dividing by a hundred to figure out the mass or the volume or whatever of a smaller number of objects