How to Convert!

Yesterday in class, to sum it up, all we did was convert.  Converting here, converting there. And of course, we learned different ways to do it.  

Kill Him Dead But Don't Call Me?

The first and most basic way to convert is the way almost all the elementary teachers teach it. 

KHDU(or B)DCM, or King Henry Drinks Unlimited Delicious Chocolate Milk.  I've even heard of Kill Him Dead But Don't Call Me.  That was a pretty odd one, but that's besides the point! This trick however, actually stands for the way to convert between metric units.

Kilo Hecto Deca Unit(or Base) Deci Centi Milli

All you do is take your given number, let's say 6 meters, and slide it along this set of letters.  6 meters is a unit or base, so you would start at U (or B).  You would then jump from letter to letter, moving the decimal point of the number as you go along, until you reach the unit you are converting to.  If you convert 6 meters to kilometers, you would move the decimal 3 places to the left, making the new number 0.006 kilometers.  If you converted 6 meters to millimeters, you would move the decimal 3 places to the right, making it 6,000 millimeters.  This does make logical sense though, because when you convert to a smaller number, the resulting number should be greater, and vice versa.

What, There's More!

Just when we thought we had it down, my teacher throws us a curve ball.  "Wait there's more!"  It sounds just like a TV commercial to me.  "Don't forget that for a special price, we'll throw in more units! So get to work now!"  I knew it.  I knew there was something else.  

According to this commercial, the KHDU(or B)DCM doesn't really work as great as you might assume. Yay... not.  That means that there are more units than just what is on this conversion method.  And, guess what, it takes extra work as your special price!  It would actually look like this:

...Tera Giga Mega Kilo Hecto Deca Unit Deci Centi Milli Micro Nano Pico...

Plus, it gets more confusing!  First of all, it goes on forever, and second of all, once you get past Milli or Kilo, you can no longer do the sliding decimal method.  It turns out that, once you get past the two, there is actually 1,000 in each.  I know that sounds a little weird, but by this I mean that there are 1,000 kilometers in a mega meter, for example.  Now, the only problem is how to convert to these bigger numbers.

New Methods

Our teacher told us about two ways to convert between numbers instead of KHDUDCM.  Now, we can use Dimensional Analysis or cross-multiplying.

Cross-Multiplying

This is the first way we learned, which is kind of easier.  It is basically a one or two step process of multiplying two fractions or ratios, but not across. You would multiply diagonally. For example:

6/2 = x/2

You would do 6 times 2 and x times 2 making, your answer be 12=2x.

You would then divide by 2 and find your answer of x to be 6.

To convert for this problem, let's say you were converting from 2 feet to x inches.  You would set up a proportion of 2ft./x in. = 1ft./12 in.  This way,you would only come out with inches in the end.  However, this method does have its drawbacks.  For example, you cannot convert between multiple units at the same time. That's where Dimensional Analysis comes in.

Dimensional Analysis

The second way is this Dimensional Analysis method.  This way, you can keep things organized easier and convert between multiple units at the same time.  However, this way, you have to multiply across, not diagonally, and you must have the same units opposite each other so they cancel and you are only left with the units you want.  Let's say you were converting from 32km./hr. to x mi./hr. :

32km/1hr = 0.6214mi/1km = 1hr/60min. 

You would then multiply across and get 19.8848mi/60min.  This is because the km and hours would cancel and you would only be left with the units you want to get to.

Then, you would simplify to get it to x miles for every 1 hour getting 0.33mi/hr as your final answer.

Personally, I find this method to be easier.  It is easier for me to see visually and it is easier for me to check to make sure I did my work right.  However, it all depends on what is better for you. 

Also, as a little side note, when rounding, you need to round to the most appropriate number.  If the number you are coming from, like 32km, is rounded two digits already, then your answer should be rounded two digits as well.  Also, the more decimals there are, the more precise the number is. 32.0000000 is more precise than just 32.

Reflection

I think I am still doing a good job in class.  I participated in class and helped out in my group discussions.  I also have decided to do dimensional analysis as my main method because it's easier.  I have just now realized that I should be working on the things that work better for me, not the confusing way.  I believe that you should still try to understand the more confusing way, but if you just can't get it, you shouldn't force yourself to do it.