Unit conversion problems come up a lot in science. Sometimes you hear this style of
problem solving called “Dimensional Analysis.” This is an approach to problem solving that
involves using conversion factors and making sure your units cancel. The trick is to look
at the units you start with, look at the units you want to end up with, and use a conversion
factor to get there. starting unit x conversion factor = ending unit.
The conversion factor looks like this: ending unit over starting unit.
So see how starting unit and starting unit cancel to give you the ending unit.
Sometimes, you may need two or more conversion factors - we’re going to save that for the next video.
A conversion factor is a fraction that equals one. Like, 12 inches over 1 foot is a conversion factor.
12 inches is the same as 1 foot, so 12 inches divided by 1 foot equals 1. So if
you multiply your original value by a conversion factor, you don’t change its value - because
you are just multiplying by 1 - you just change the units.
We could use this conversion factor to go from inches to feet, or from feet to inches.
Let’s say I started with 36 inches, and I wanted to know how many feet that was. I
know that 1 foot has 12 inches, so I can write that as a conversion factor
1 foot / 12 inches Now I can multiply these together, making
sure my units cancel. 36 inches x (1 foot/ 12 inches) = 3 feet
Notice that I wrote the conversion factor with feet on top, and inches on the bottom,
because I wanted inches to cancel, and I wanted feet in my final answer.
What if I wanted to convert in the opposite direction? What if I know something is 5 feet
long, but I want to know how many inches that is - I can use that same conversion factor,
just flipped. I don’t have to memorize how to set up the problem - I just make sure the
units cancel. I start with 5 feet, multiply by the conversion
factor so feet is on the bottom, so it will cancel, and inches is on the top so it will
be the final units in my answer. 5 feet x (12 inches/ 1 foot) = 60 inches
Let’s do a more typical example problem - something you couldn’t figure out in your
head right off. If a man has a mass of 75.0 kg, what is his mass in lbs?
Write what you know on the left 75.0 kg
and write what you want on the right. = some number of lbs. Leave a little room
for the conversion factor. We will multiply by a conversion factor to
change the units from kg to lbs. Remember, the conversion factor has to be
equal to 1.
I would look this conversion factor up, because I probably don’t know this off the top of
my head like I do the conversion factor 12 inches for every 1 foot. Okay, so I look it
up, and I find that there are 2.2 lb in every 1 kg. Let’s write that as a fraction equal
to 1. 2.2lb/1 kg
As it turns out, we wrote that fraction in just the right way to solve this problem.
Can you see that it would NOT be the right order if I wrote it as 1kg/2.2 lb? That fraction
equals 1, but the units wouldn’t cancel in our problem. So let’s take that out and
put it back the right way.
75.0 kg x (2.2 lb/1kg) = some number of lbs
You can see that the units cancel - kg cancels kg, and we will just be left with lbs, which
is what we want to be left with in our final answer. Multiply across the top and bottom.
75.0 x 2.2 = 165.0 lb make sure you write in the units.
Don’t forget to check for # of significant figures. We had 3 significant figures in 75.0,
so we can write 3 significant figures in our final answer. 165 lb