dimensional analysis help, i'm just not getting this, if anyone knows an easy (4th grade) way to explain or remember whn and how to use conversion factors I would much appreciate it.
May 31, '04
If you know what units you shoud end up with, just make sure everything else cancels out, leaving the correct units.
Example: Convert 100lbs to kg
If 1 kg = 2.2 lbs:
(100 lbs X 1 kg)/2.2 lbs = (100 lbs X kg)/2.2lbs = 45.5 kg
(lbs cancel out)
Last edit by stsdoc on May 31, '04
May 31, '04
OK, first -- please IGNORE THE DOTS BELOW. The computer wouldn't let me use the space bar to create crosses, so I had to use dots in order to place numbers/bars in the correct places. Please try to visualize all this without the dots:
It's easier if you draw a cross first: ____I____
In the upper left hand corner, place the number that needs to be converted. For example, "4.4 pounds = how many kilograms?" -- In this question, the 4.4 needs to be converted from lb's to kg's.
Do NOT put anything in the lower left hand corner. This one is ALWAYS blank. Next, determine what you need to convert 4.4 lb's into. According to the question, you want to know the number of kilograms. What is the conversion factor? According to most nursing books, it is important to know that 2.2 lb=1 kg. Therefore, this is your conversion factor. OK, now you want to eliminate the lb's in your equation and have "kg's" for an answer, since that's what the orginial question above asks. Since equal units can be crossed out DIAGONALLY, you will need to place the "2.2 lb" diagonally to 4.4lb in your equation:
See how 4.4 is diagonal to 2.2? The 1 kg is above the 2.2 b/c they go together (they are the conversion factor, ie. 2.2lb=1 kg and 1 kg=2.2lb). Now, CROSS OUT PAIRS OF UNITS. There is only one pair, "lb". Cross out both of the lb's. Now you only have a single "kg" left. That's good, for you want your answer to be in kg's. After crossing out your units, look at the numbers. Multiply the top & divide that by the bottom (ie. 4.4 X 1 = 4.4. Now divide that answer by the denominator, or 2.2. The final answer is 2). Finally you see that your answer is 2 kg's.
This same procedure can be used for multiple conversion factors. For example, "how many seconds in 4 hours?"
____4 hrs____I____60 min____I____60 sec____ = ?
...........1.......I........1 hr........I........1 min
Do you see how "4 hrs" goes in the upper left hand corner b/c it's the known variable? The rest are two sets of conversion factors (ie. 60 min= 1 hr; 60 sec = 1 min). How did I know to place them in this order? B/c I can only cross out units DIAGONALLY. Since I want to get rid of "hrs" and move to "seconds", I need to arrange it in the above way. Do you see that after crossing out pairs of units, I only have "sec" left? That's what I want, for the original question asks for seconds.
Multiply the numerator: 4 X 60 X 60 = 4 X 3600 = 14, 400
Multiply the denominator: 1 X 1 = 1
Divide num by denom = 14400/1 = 14,400 seconds
Last edit by lady_jezebel on Jun 1, '04