Hey, guys. So now that we've seen SI units in the SI unit system, a lot of times you're gonna see letters or symbols that get 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, or metric units. So we're gonna see letters like k or m or even Greek letters like mu. These are called metric or SI 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 for milli, or mu for micro. And each one of these prefixes or letters just stands for a specific power of 10 that you're gonna multiply by a base unit. So for instance, kilo is 103. Micro is 10-6. 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, 5 kilometers or 5 kilometers 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 103 or 1,000, means the same thing. So 5 kilometers just means 5 times 1,000 meters. So 5 kilometers is just the same thing as 5,000 meters.

Here's another example. 4.6 ms. 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're gonna look up this m and m stands for milli. And this milli prefix stands for a specific power of 10, 10-3 or 1,000. They're 0.001. All those things mean the same thing. So 4.6 milliseconds just means 4.6 times 0.001 seconds. So these prefixes just help us write these numbers in just a more compact way. So we're gonna use this table a lot actually because you're gonna have to convert between the metric prefixes. 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 to m. Here's the first thing you're always gonna do when you're rewriting these using metric prefixes. You're gonna identify where your starting and target prefixes are. So here, I'm starting at h. So h stands for hecto. And then I'm actually going to no base unit. So I'm actually going to no prefix. So that's actually I'm sorry. No prefix. So that's the base unit. So I'm really just going from here to here. So what I have to do 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 hecto to base unit. So I'm going from 102 to 100. So if I move from here to here, then I've jumped 2 exponents. So I've really gone 2 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 gonna shift the decimal place in the same direction that we moved in step 2. So for example now, 6.5 hm, we shifted 2 to the right. So in terms of meters now, you just take the decimal place and you shift it to the right twice, and you fill in a 0 as needed. So 6.5 hectometers is the same thing as 650 meters. That's really all there is to it. Just follow these steps and we'll 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, M. So this is milli, 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 milli and I wanna go towards the base unit. So I'm just gonna go from start to finish, or from start to target, and I'll count up the number of exponents that I moved. So I'm going from 10-3 to 0. Just look at the number. Don't worry about the sign. We actually jumped 3 to the left. So from here to here, we jumped 3 to the left. So that means that 3.89 millimeters if I wanna 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 it to the left because that's the same direction I moved in step 2. So 1, 2, 3. And so, I'm gonna fill in zeros along the way, and then I'm gonna put another 0 point, so that the decimal point is, like, right here. So that's 0.00389 meters, and that's our answer.

Now for this last one here, we're gonna convert or we're going to rewrite, 7.62 kilograms to micrograms. So here, we just identify the prefixes. I'm going from kilo, and then eventually, I'm gonna end up at micro. So here's what I'm gonna do. I'm gonna shift from start to the target. So from 103, I'm gonna have to cross through the 0 exponents. So when I move in this direction, I'm actually going 3 exponents. And then from 0 over to micro, which is 10-6, then I'm jumping actually 6 exponents. So in total, I've actually moved 9 to the right. And so, therefore, I'm just gonna shift the exponent to the right 9 times. So 7.62 kilograms becomes I'm just gonna shift it 1, 2, and then 1, 2, 3, 4, 5, 6, 7. So it's 1,2,3,4,5,6,7,8,9, and I'm gonna fill in 7 zeros along the way. And so that is how you would convert how you would rewrite 7.62 kilograms to micrograms. So we can see here like kind of a pattern. And so when you're rewriting these numbers with, with metric prefixes, there's a pretty easy rule to follow to 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 your 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.