Eidolon wrote:
*blinks* I'm doing Dimensional Analysis in math currently. It's nothing exceedingly hard, and I can do the really easy inches --> feet and meters ---> kilometers etc, but...I'm having trouble with the only-slightly-more-difficult ones. Which bothers me because normally math is easy for me, but for some reason I just can't wrap my mind around it.
For example, some of the problems on tonight's homework:
500mm^2 = ?cm^2 (I think I got that one right, not sure)
840in^2 = ?ft^2
2km^2 = ?mm^2
Those are just a few examples of the problems. I don't want the answers, I could find those easily enough with an online conversion thing, but I just...don't get it. I know that to get feet to inches you multiply by 12 and to get 2ft^2 to ?in^2, you have to do 12 x 12 x 2, etc, but I don't know why and as a result I can't apply it to other problems. I want to understand it, not know how to do the easy ones and then get lost on the harder ones.
Someone help?

I'm guessing what you want help on is why in order to get something like 2ft^2 to ?in^2 you'd have to do 12x12x2. Right? I'll build on that.
You know how in each foot you got 12 inches, right? So if you have 12 sq. inches in a row you've got something like this:
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right? That also is a foot, right? So a sq. foot looks something like this then:
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Because that's so complicated and has too many @s in it, let's make that big giant thing equal this:
+
So now our sq. inch looks like @ and our sq. foot looks like + even though that's actually twelve @s by twelve more @s.
Now if you have ++ (2 sq. feet, yes?) then you've got two of those big giant 12x12 @s next to each other.
You've got 12x12x2. The 12x12 comes from the fact you've got 12 inches in a foot and another 12 inches in a foot and then two such squares next to each other.
So for something like mm^2 to cm^2. You have a 1 sq. mm thing that looks like @ and a 1 sq. mm that looks something like:
@@@@@@@@@@
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That's 100 mm, right? 10x10, yes? 100. Let's make a sq. cm an + now that we know what it looks like.
So if we know that something like that is 100 sq mm. Then we can figure out how big 500 sq. mm is. That looks like +++++ right? Because there's five 100s in 500.
So if you know how many sq. inches are in a sq. foot or sq. mm in a sq. cm or something like that, you can figure it all out. But that's because we know the definition of a square foot is a square with side length 1 foot by 1 foot. And because 1 foot = 12 inches, that square also equals 12 inches by 12 inches.
Then if you want to do things with bigger units and smaller units (ie: meters and mm), figure out what it would be with units in between instead. So using that example (meters and mm), we start by knowing a sq. mm looks like @ and a sq. cm looks like 10 @s by 10 @s, or a +. And because we know that a meter has 100 centimeters, we can put 100 +s in a row by +s in a row (that probably won't fit here). And we'll have a square meter. But that doesn't solve the problem of how many sq. mm there are in a sq. meter yet, does it? So we go on.
Let's take a single row of that sq. meter. We've then got 100 +s in a row. How many mms can go across it then? Well, if a + is actually 10 @s, we can do 100x10 (100+ times 10@) and get 1000. So now we know there's 1000 mm in 1 meter. We can then go on and do 1000 mm x 1000 mm to get how many sq mms are in a sq m. That's 1000000 sq mm in 1 sq m. You can go onto even bigger things if you wanted to, but I'll stop at that point.
Don't feel afraid to draw pictures all over your math textbook or whatever you happen to be using. I do it all the time even though I'm not supposed to. And people before me have, which means that some things are in pen, some things are so erased you can't see it. If you happen to be one of those people who have the luck of having pictures in your textbook, copy them onto another piece of paper if you're afraid of writing on the book by just laying a piece of paper over it. Trust me, work with drawings. It makes life easier. Or if you're someone like me, work with @s and +s.
And if you're still confused, draw pictures! Lots of pictures. Squares! Those aren't too hard to draw (unless you're trying to make them perfect). I hope I helped clear things up rather than confuse...
If you happen to want to know the answers to your problems there, highlight the following:
Quote:
500mm^2 = 5cm^2
840in^2 = 5 5/6 ft^2 or 5.83 with a bar over the 3 or 35/6
2km^2 = 20,000,000mm^2
Iced - Silver [dot] Net ... now go. And maybe someday I'll actually get up something that resembles a pretty sig.