Leah here from leah4sci.com and in this video we're going to continue our discussion on
dimensional analysis unit conversions specifically looking at problems that involve more than
one conversion. You can find part 1 along with the unit conversion practice quiz and
SI units to memorize for the MCAT cheat sheets on my website leah4sci.com/conversions.
In part 1 we looked at the setup of given times ratio to help you take the units from
where you are to the conversion of where you need to go. But we kept the conversion simple,
from one unit to another. For example, say we're given 24 meters and we're ask to convert
it to kilometers, we set it up with a given, in this case 24 meters, times a ratio that
has the unit for the given in the opposite numerator or denominator so that we can cancel
it out. Here we would put it in the denominator and then the unit we're trying to get to,
we put in the numerator. Assuming there is a direct conversion between them. How do we
convert from kilometers to meters? We know that 1000 meters is equal to 1 kilometer so
we set it up as 1 over 1000. This allows us to cancel out the units leaving us with the
math of 24 times 1 over a thousand. You should know how to do this using the move the decimal
trick that I teach in the MCAT Math Series, leah4sci.com/MCATMath. For every zero in the
denominator we kick the decimal and move it back one space so that gives us one two three
with an answer of 0.024 kilometers which you can also represent in scientific notation
as 2.4 x 10 to the minus two. How do we get this answer? If we move this back one, two
spaces we get a whole number decimal the rest of the unit, 2 spaces back is 10 to the minus
2. Another way to do this is to recognize that a thousand ten to the third and that
means we have 24 divided by ten to the third. If we write that as 24 times 1 times 10 to
the minus 3 because 1 over ten to the third is one times ten to the minus three. Then
we simply do the move the decimal trick, again taught in the Math series. In this case we
move the decimal to one smaller so we make this one, 1 bigger, goes from 24 times 10
to the minus three to 2.4 times ten to the minus 2 that we have here. Again, this was
just review. If you were uncomfortable with a setup or the Math, make sure to review the
appropriate videos that are all linked below so that you can understand what we do in the
next step when we start adding multiple steps to each conversion.
For example, say you're told that a vehicle is moving at a velocity of 47 meters per second
but you wanna convert this into kilometers per hour so you setup your equation as given
times ratio but then what do we fill in? The given in this case is 47 meters per second
but now we need a ratio that allows us to have meters to cancel out or seconds to cancel
out, which one? And the answer is we want both but we can do it one at a time. Remember
that with multiplication, if you have a unit times another unit times another unit, the
order ultimately doesn't matter because the answer will still be the same no matter what
order you use to multiply. So when you have multiple conversions just treat it as one
conversion at a time. Going for 47 meters per second, we're really trying to convert
meters to kilometers and we're trying to convert seconds to hours and so we just take the steps
to go from one to the next to the next as a given times a ratio times another ratio
times another ratio. Let's move it over so we have room starting out with 47 meters per
second, let's choose meters to convert first, we wanna go from meters to kilometers. We
have two options, we can say that 1000 meters is equal to 1 kilometer or that 1 meter is
equal to 1 times 10 to the minus 3 kilometers. I know a lot of students get confused here,
so here is how I think about it. I have many small equal one big, right coz that one big
is so big it has many smaller pieces in it but if I'm looking at just one small,it's
gonna be a tiny tiny portion of that giant unit, so 1 meter which is small compared to
a kilometer is a tiny tiny portion 1 times 10 to the minus 3 of that giant thing. Which
one do I prefer? I like to avoid scientific notation as much as possible, I like to avoid
decimals and fractions, I like my numbers to be clean so this is my preferred method.
If you're asked to do this in scientific notation you can also look at this as ten to the third
meter is equal to one kilometer and the reason I point is out is if we have to use scientific
notation I don't like the negatives. How do we get the positives we just look at the opposite
direction. A lot of small is equal to one big and it's all positive values. Both are
correct it's really just about what's simpler and faster and most importantly, less confusing.
The less confused you are the more confident you will be going through the problem.
We're doing a conversion of meter so we're gonna put meters on the bottom, let's go with
1000 meters is equal to 1 kilometer, I like to cancel as I go. When you're just learning
this, write it, cancel so you'll know you're on track and we have a unit that we want.
So this one we'll leave alone, next we go to seconds. For seconds we don't have direct
conversion to hours. We know that 60 seconds is equal to 1 minute, so let's set it up with
seconds on top allowing us to cancel that means we have 1 minute on the bottom, 60 seconds
on top. Seconds cancelled out, minute is not the unit we want so we need one more step
for this conversion and that conversion is going to be 60 minutes is equal to 1 hour
which goes on top which goes on bottom, we need minutes to cancel. So minutes go on top
allowing hour on the bottom, 60 minutes, one hour, minutes cancel. The only units remaining
are kilometers divided by hours which is perfect because we're trying to find the answer in
kilometers per hour and then we have the Math. Again that's 47 times 60 times 60 divided
by 1000. On MCAT you can't use the calculator but on the MCAT , close enough is good enough
so let's see how we can simplify it. First thing I'm gonna do is knock out my zeros,
one from the top and bottom, another from the top and bottom, this gives us 47 times
6 time 6 divided 10. Let's do a quick rounding, 47 rounds up to 50 which gives me another
zero to knock out, that means I have 5 times 6 times 6 divided by 1. 5 times 6 is 30 times
another 6, I don't know but I know that 6 times 3 is 18, add that zero back, the answer
is 180 or approximately 180. The calculator gives me an answer of 169.2 which is on the
MCAT is close enough.
Now here is one trick you could have applied. Given that 60 seconds is 1 minute and 60 minutes
is 1 hour, if you see that conversion over and over and over, you may as well memorize
that 36 hundred seconds is equal to 1 hour. Another confusing type of problem is when
you are forced to use exponents but you have been going in multiple directions meaning
you have multiple steps with exponents. For example, if we look at a Bacterial Cell, which
is about a 10th of the size of an animal cell and yes you need to know this for the MCAT.
Say you're given a specific bacterial cell that is approximately point two microns in
length and you are asked to convert this into kilometers. We setup our equation as Given
times Ratio. Knowing that our given is 0.2 microns. What the heck is a micron? It's just
a fancy short way of saying micrometer which you can write like this, which is u m or you
can just write it as u m if you're trying to type it out. So we have point two micrometers
and we wanna convert that to kilometers. I don't know about you but I don't know the
conversion between micrometers to kilometers but I do know how to go towards meters because
you should have memorized according to the cheat sheet link below how to go from meters
to everything else. Meters to micrometers, to millimeters, to kilometers, and so on.
So let's set this up as given times multiple ratios. We have .2 micrometers and the first
thing we wanna convert to is meters so we're gonna go from micrometers to meters keeping
in mind the following conversion; 1 times 10 to the sixth micrometers is equal to 1
meter or 1 micrometer is equal to 1 times 10 to the minus six meters. Again a whole
lot of tiny is equal to 1 big or 1 tiny is a tiny, tiny portion of that big. This is
where a lot of students get confused, make sure that you understand that it can't be
the other way around. You can't have 1 micrometers equals to 1 times 10 to the 6th meter coz
you'r saying one tiny is equal to a whole lot of huge and that just doesn't work. Which
one do I wanna use? I don't like negative exponents if I can avoid them so I'm gonna
take the first one and say that 1 meter is equal to 10 to the 6th micrometers, where
that 1 is self understood so you don't have to include it. This allows us to cancel out
the micrometers taking us to the next conversion from meters to kilometers which we already
absolutely know. In this case we can use the exponents or use a thousand given that we
already have one exponents and they're fairly easy to add, let's go ahead and put exponents
on the bottom for the other one. 1 kilometer is equal to the 10 to the third meters, this
allows us to cancel meters leaving us with our desired unit for the answer kilometers
and now we just have to carry out the math.
The Math itself is 0.2 times 1 times 1 which doesn't change, divided by 10 to the 6th times
10 to the 3rd. First combine the unit on the bottom 10 to the 6th and 10 to the 3rd is
equal to 10 to the 9th because when you multiply all you do is add the exponents and I'm gonna
write this out but I want you to do this in your head. Point two is really 2 times 10
to the minus 1 and a number divided by 10th to the 9th is really 1 times 10 to the minus
9 so we can think of this as 0.2 times 10 to the minus 9 but for proper scientific notation
you need this number to be one whole number and then the decimal. So we have to multiply
this by 10. We're using that times 10 divided by 10 trick again. We multiply it by 10 to
give us 2, that means we have to divide this one by 10 because if we make one bigger we
have to make the other one smaller giving us to the minus ten for a final answer of
2 times 10 to the minus 10 kilometers. Again, if the Math at any point was overwhelming
especially the tricks make sure you go back and study the MCAT Math without a calculator
tutorial series. If you were able to follow the Math and the concepts but want more practice,
make sure you try the dimensional analysis unit conversion quiz which I have linked below.
You can also find it on my website leah4sci.com/conversions.