Okay so we’re gonna talk about now is:
converting units, and we talked about this before. This is more converting units squared is it really what I want to be talking about. Converting squared units is just like converting normal units except they’re squared, yeah. That’s goofy to say. So say we have 300 centimeters squared(²), and we want to convert that to feet squared. You can go ahead and do the little ratio thingy like we’ve been doing, but what you want to be careful of is that you actually square all your ratios. So we can say “Well I want to convert centimeters to inches and there is 1 inch in 2.54 centimeters, but I don’t just have centimeters, I have square centimeters. So I’m gonna put little twos (²) on everything. All right then I want to convert inches into feet, so I’m gonna convert inches into feet, and I know that in 1 foot there is 12 inches. There is 12 inches. I am automatically fantastic, so we’re gonna put little Squared’s on everything. So now as we look, we can say “okay I have centimeters squared cancels with centimeters squared. Inches squared cancels with inches
squared. So I’m just left with feet squared which is what I want. So I’ve got 300 times 1². We all know 1 squared is 1, so I’ll just leave that. Hey, so got 1 times 1 on the top and feet squared, and then 2.54² times 12². So what I’m going to do is I’m gonna get my calculator, I’m gonna go 300 divided by 2.54² divided by 12² so 300 divided by 2.54² divided by 12² and I’ll get 3.22917.. whatever. 3.22917 ft² and because let’s make sure
I did that right. So what, it was 3.22 Because I don’t want to be obnoxious and have more, what’s it called, significant digits, than I actually need. I’m gonna just round it off to three significant digits. So one, two, three. Pull this one out, it’s a 9. 9 is greater than 5 so I round up, and so this becomes … the three, the two becomes a three. Everything else goes out to zero but it doesn’t matter because they’re not significant, so I don’t include them anyway. And that gives me: 3.23 feet². Question is, well why does it matter why do I have to square all this junk anyway? Shouldn’t it just work out? The answer is not really, no. So say if you decided not to do this, and you said “well I’m gonna go 300 centimeters squared and there’s 2.54 centimeters in an inch. and there’s 12 inches in a foot. Well first of all, what’s happened now you’re inches do cancel out, which I guess is okay, and one of your centimeters cancels it out. So what you really got, not only is mathematically wrong, but physically nonsense. You have 300 divided by 2.54, divide by 12 centimeter feet. Which is not what you want, and if you actually work that out, so you have 300 divided by 2.54 divided by 12, which would be 9.8 something. Whatever, but the point is whatever that
was, 9.84, you know. 9.84 centimeter feet which really doesn’t mean anything. So it’s very, very important that you do remember to put the squares (²) on these things when you’re converting these squares.