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Metric Prefixes

Patrick Ford
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Hey, guys. So now that we've seen s I units in the S I units system, a lot of times you're gonna see letters or symbols attached to your base units. Your base units are just meters, grams and seconds. They're kind of like the most simplistic basic units of metric units. So we're gonna see letters like K or M or even Greek letters like mu. These were called metric or S I unit prefixes. And the basic idea is that each one of these letters is just a shorthand for a prefix like K for kilo M family arm you for micro. And each one of these prefixes or letters just stands for a specific power of 10 that you're gonna multiplied by a base unit. So, for instance, kilo is 10 to the third Micro is 10 to the minus six. They're kind of just like easy ways to represent big and small numbers. So you don't have to write a bunch of zeros out. For example, five kilometers or five k m is gonna be. If we wanted to represent that in terms of meters, we would just look up k inside of our table. We know K stands for Kilo and the prefix kilo stands for 10 to the third or 1000 means the same thing. So five kilometers just means five times 1000 m. So five kilometers is just the same thing as 5000 m. Here's another example 4.6 m s. So here we're gonna look up this prefix M which, by the way, is not the same thing as our base unit of meters, same letter, but different meaning. So we look at this M in M stands for Millie. And this Milly prefix stands for a specific power of 10 10 to minus third or 1/1000 10.1 All those things mean the same thing. So 4.6 milliseconds just means 4.6 times 0.1 just multiplying by a specific power of 10. And so this number here just ends up being 0.46 seconds. So these prefixes just help us write these numbers in just, um, or compact way. So we're gonna use this table a lot, actually, because you're gonna have to convert between the metric prefix is. So I'm gonna give you a really simple process for doing this. Let's just do a bunch of examples and see how this works. So we're gonna express the following measurements and we're gonna basically rewrite them in the desired prefix. So let's just get to the first one. We're gonna convert 6.5 h m to M. So here's the first thing you're always going to do when you're rewriting these using metric prefix is you're gonna identify where you're starting and target prefixes are so here. I'm starting at H, so h stands for Hecht. Oh, and then I'm actually going to know base unit. So I'm actually going to know prefix. So that's actually I'm sorry. No prefix. So that's the base unit. So I'm really just going from here. Thio here. So what I have to dio is the next step is I have to move from the start to the target, and I'm just gonna count up the number of exponents that I moved. For example, I'm going from Hecht oh, to base unit. So I'm going from 10 to the to 10 to 0. So if I move from here to here, then I've jumped two exponents. So I've really gone to to the right here. And it's important that you figure out the direction because that leads us to the third step, which is we're going to shift the decimal place in the same direction that we moved in Step two. So, for example, now 6.5 h m. We shifted to to the right. So in terms of meters, now you just take the decimal place and you shifted to the right twice and you fill in a zero as needed. So 6.5 Hecht 0 m is the same thing as 650 m. That's really all there is to it. Just follow these steps and will always get the right answer. Let's just do a few more so we get comfortable with this So 3.89 millimeters to meters. So here we have this prefix, uh m eso This is Millie and we're gonna go to the base unit which is in meters, so we're gonna do the exact same procedure here. I'm starting off at Millie and I wanna go towards the base unit, so I'm just gonna go from start to finish or start to target, and I count up the number of exponents that I moved. So I'm going from here to here, and I'm going from 10 to the third of minus third 20 Just look at the number. Don't worry about the sign. We actually jumped three to the left. So from here to here, we jumped three to the left. So that means that 3.89 millimeters If I want to write this in terms of meters, I'm gonna write the number 3.89. But I have to shift it to the left three times, right? So I have to shift to the left because that's the same direction I moved in Step two. So 12 and three. And so I'm gonna fill in zeros along the way. And then I'm gonna put another zero point so that the decimal point is like, right here. So that 0.3 89 m and that's our answer. Now for this last one here, we're gonna converts, or we're going to rewrites 7.62 kg, Two micrograms. So here we just identify the prefixes I'm going from kill Oh, and then eventually I'm gonna end up at Micro. So here's what I'm gonna dio I'm gonna shift from start to the target. So from 10 to the third, I'm gonna have to cross through the zero exponents. So when I move in this direction, I'm actually going three exponents and then from zero over to Micro, which is 10 to the minus six. Then I'm jumping, actually, six exponents, So in total of actually moved nine to the rights. And so therefore, I'm just going to shift the exponents with right nine times. So 7.62 kg becomes I'm just gonna shift it. 12 and then 1234567 So it's 123456789 I'm gonna fill in seven zeros along the way. And so that is how you would convert how you would rewrite 7.62 kg, two micrograms so we can see here. What kind of a pattern? And so when you re writing these numbers with with metric prefix is there's a pretty easy rule to follow to kind of check. You know, if you're if you're doing the right thing, if you're shifting from a bigger to a smaller unit basically going to the right, Then your number is going to become larger. So if you're units are becoming smaller, there should be more of them. That's the way to think about that. And if you're going from a smaller to a bigger unit, then your number is going to become smaller. Alright, guys, that's it for this one. Let me know if you have any questions.