One of the most useful skills that you
can pick up, in scientific quantitative analysis,
Is the ability to look at and manipulate
the units that are attached to the numbers.
This is called the factor-label method.
And once you get it, it seems very intuitive, but it seems to me
that nobody is born knowing how to do this, so you
might have to work at it a little bit to get it.
Say we have a number which is a velocity in units of kilometers per hour.
And then we want to convert that into different units of meters per second.
Instead of trying to remember a formula to do that, we
can actually use the kilometers and the hours, meters, and seconds.
To construct the formula that we need to do the conversion such
that it will make the units work.
So we'll start with a velocity in kilometers
per hour, say we're driving along and it's
100 kilometers per hour, and you want to know how many meters per second that is.
So, we need to find factors that can
convert these units into the ones that we want.
And so let's start with the time units.
We want to convert from hours to seconds. And so we'll start by writing a factor
which can cancel out the units of hours here, and give us something shorter.
And I don't remember in my head how many seconds
there are in an hour, so I'll write it out.
Do this in two stages, that there are 60 minutes
in an hour, and so now we can cancel the
units of hours here and that's the first step in our
our factor label method. Now because an hour equals 60 minutes.
If you take a quantity which is the same on the top and the
bottom of a fraction, then that quotient is equal to one.
So by multiplying our
original information, which is 100 kilometers
per hour, by this conversion factor, we're
just multiplying by one, and so we're not actually changing the value at all.
We're changing the units and so that changes
the numbers, but the actual quantity stays the same.
So the next factor will be from minutes
to seconds, where 60 seconds equals one minute.
Now the minute units are gone away and we have kilometers per second,
so that's getting closer, but now we have to deal with the kilometers to meters.
And so the conversion factor here is a kilometer is equal to 100 meters.
And I have to put the kilometer on the bottom
I can see, because I have to cancel kilometer here.
And end up with meters on the top.
So after we have constructed this whole thing to cancel out the units.
It's meters.
So we're left with what we want, meters per second.
all we have to do is multiply the numbers.
100 times 1000 divided by 60 divided by 60 gives us this answer.
And so the units have told us how to do the math.