Leah here from leah4sci.com and in this video we're going to look at a simple approach for
dimensional analysis or unit conversions so that if you're doing Math on the MCAT you
can quickly and easily know exactly what to convert and of course you can apply this to
your Chemistry and Physics classes as well.
You can find pre-unit conversion practice quiz and SI units to memorize for the mcat
cheat sheet on my website Leah4sci.com/Conversions.
When you first learn dimensional analysis, you learned a complex definition about going
from one unit to the other as long as everything balances and we're gonna get back to that.
But you also learned a lot of memorization.
For example, you're given 36 grams of H2O and told to convert it into the number of
moles or convert it to the number of molecules or the number of hydrogen atoms.
You probably memorized a conversion factor.
But the problem is when you're doing a conversion like this, a lot of times I find myself stuck!
If I have 36 grams of H2O and I know that there are 18 grams per mole, do I multiply
by 18 or do I divide by 18?
If you memorized it, you risk getting confused and I always got confused.
What we wanna do is figure out a way that you don't have to think about it but instead
you simply look at it and you know exactly what type of Math to do based on what you're
given so that you can quickly move out to the next step and the next step.
Say you're given seven minutes and you're asked to convert this into seconds.
You know that there are 60 seconds in 1 minute so do you set this up as 7 minutes multiplied
by 60 seconds or divided by 60 seconds, same question.
The trick I'm going to show you takes a while to learn but it's very fast and easy to apply
once you get it.
So bear with me as we slowly build up the logic step by step so that once you get it
you can quickly and easily apply it to any Chemistry, Physics, or conversion problem.
Why?
Coz on the MCAT, you don't have a lot of time, you definitely don't have a calculator so
you need to get past it quickly.
And the shortcut comes from the multiplication property of one.
Any number multiplied by one is equal to itself.
So if I have one times one, it equals one.
If I have two times one, equals two.
One hundred and seventy five times one equals one hundred and seventy five.
Again, the number multiplied by one equals itself.
But it doesn't have to be a simple number that you recognize, for example, you can take
a duck multiplied by one and you get a duck.
You can take a pencil, multiply that by one and you will get a pencil.
It doesn't matter what you multiply or how it appears so long as you multiplied by one
it stays the same.
Simple enough so far?
Let's take it one step further.
What if I introduce fractions?
A number divided by itself is equal to one.
So one over one is equal to one.
Two over two is equal to one.
175 over 175 once again equals one.
But if I change the number two times one over one, it's just 2 times 1 equals 2.
2 times 175 over 175 is just 2 times 1 and that's still equals to 2.
Any number divided by itself is equal to 1 so that if you take a number and you multiply
it by a fraction that consist of a number divided by itself, it's simply equal to that
number because the number times 1 equals that number.
It should feel very very simple up to this point but I wanna make sure it's crystal clear.
What if we take it a step further?
What if we change the fraction so that what we put on top or the numerator is slightly
different or looks slightly different than what we put on the bottom, the denominator.
But if they're still mean the same thing, it's still equals 1.
A pair over 2 is equal to 1 coz there's two in a pair.
If I flip it around and I divide 2 over a pair, that's still two over two, a pair is
two and that means it equals to 1.
What if I take a dozen and I divided it by 12?
A dozen is twelve, that's equal to one.
And if I flip it 12 over a dozen, that's again, 12 over 12 equals 1.
Up to now we're looking at just numbers but for dimensional analysis, we need units as
well.
If the numbers are different, with the unit of 1 equals to a different number of another
unit, we still get the same thing.
For example, we discussed time as minutes and seconds.
We know about one minute is equal to 60 seconds.
How does one equals sixty it's that unit that changes the value because one is not equal
to sixty, but one minute has sixty seconds in that one minute.
So we can set it up the same way as a fraction where the top is equal to the bottom.
If we set one minute divided by sixty seconds, even though the numbers are different, knowing
that one equals the other, I can set it up with either option as the numerator or denominator
and it still equals one and I can flip it as well so I can set it as sixty seconds over
one minute and once again that is equal to one.
This right here, if you get this, you will understand the trick for dimensional analysis.
As long as what's on the top or the numerator is equal to or it converts to what's on the
bottom, the denominator your answer, your value will be the same and that means it equals
to one.
And so if I start with the number, say 9 and multiply by fractions that equal each other
until I'm blue in the face . 9 times 1 over 1 times 2 over 2 times 175 over 175, times
a dozen over twelve, times 2 over a pair, it's all just saying the same thing, 1 over
1 is 1, this is 1, this 1, 1 and one.
9 times 1 times 1 times 1 times 1 times 1 is simply equal to 9 because we multiplied
it by a whole lot of 1s.
What the heck does this have to do with unit conversions?
The idea behind unit conversions is simply converting from one type of unit and it's
giving numbers to another type.
Going back to our question of 7 minutes converting that to seconds, we need to understand that
the number for minutes is very different than the number for seconds and apply this idea
of multiplying by itself so the value doesn't change.
If I can give you 7 minutes in the equivalent number of seconds meaning the number of seconds
that exactly equals to 7 minutes, the number itself changed but the value, the true value
of the number has not change because the unit was converted accordingly.
And now you can forget all the equations that you memorized and simply remember this one
new equation.
Given times Ratio.
We are given a certain value, we need to convert it to another unit so we need a ratio that
equals to 1.
As long as that ratio equals 1, we can cancel out the units, do the math that is obvious
in front of us and convert the value.
In this case we have 7 minutes going to seconds, given is 7.
Always, always put your units, you wanna make sure you know what you're converting and also
know what to cancel.
What ratio are we going to use?
We need a ratio that converts one unit to the other.
In this case we have minutes to seconds and we know that one minute is equal to 60 seconds.
We have 2 ways of writing this equation, we can write 1 minute over 60 seconds which is
equal to 1 or we can write 60 seconds over 1 minute which is also equal to 1.
Which one do we use?
When we're setting up the ratio, let's multiply it by a fraction.
We need the unit at the bottom of the fraction, we need the denominator to have the exact
same unit as our given, this will allow us to cancel.
If we have an equation setup, minute on top, minute on bottom, that's minute divided by
minute.
Minute over minute equals one, it cancels out and whatever is left will be the right
answer.
So then we simply find the form of the equation that puts minutes in the denominator rather
than the numerator.
And here we have the second one which is 60 seconds divided by 1 minute coz 60 seconds
equals 1 minute.
The minutes cancel out and that leaves us with 7 times sixty.
You should know how to do this in your head.
6 times seven is 42, add the zero gives us 420.
The only unit left is seconds and that gives us 420 seconds equals to 7 minutes.
How do you know that you did this the right way?
How can you quickly catch that it's not the other way around?
Let's see what happens.
If we set this up as 7 minutes but use the wrong equation as 1 minute over 60 seconds,
we can't cancel anything out can we?
What we have here is 7 divided by 60.
In this case you can round it up slightly and say that's about 7 over 70 where we make
the denominator slightly larger so the answer will be smaller.
But 7 over 70 is point 1 so it'll be slightly greater than point one so let's put our answer
as approximately 0.1 but the units for the answer are minutes times minute coz nothing's
cancels that would be minute times itself or minute squared divided by seconds.
I don't know about you but I have no idea what minute square per second means and because
I can't cancel it out, I know this is wrong.
For the first one, I have minute times second over minute, and if we look at it written
out, it's minutes times seconds divided by minute.
Minute over minute cancels to give me one and that's one times second times 420 which
is just 420 seconds.
You can do this for any conversion and it will always fall into place.
Let's try this for the water example.
We said 36 grams of water convert it to moles.
How do we set this up?
Once again, given, times ratio.
In this case we are given, 36 grams of water and we wanna convert it to moles so we need
to know the relationship between grams of water and moles of water.
For this you can reference the periodic table or use the one linked in the description.
And you'll see that the mass of the Hydrogen was one, Oxygen is 16 which gives us 18.
We have one mole of water is equal to 18 grams.
We can write that one of two ways.
18 grams over 1 mole or 1 mole over 18g.
Which one do I use?
If my given is in grams then I need to be able to divide by grams.
Which one has grams in the denominator?
The second one, 1 mole over 18grams.
This allows me to cancel out the grams leaving me with just a unit of moles we're converting
from grams to moles so that's ideal.
And then we do the math!
36 divided by 18, well 18 times 2 is 36 so 36 divided by 18 is 2 and that gives me 2
moles of H2O.
At this point you either get it or you don't.
If you get it, make sure you move on to part 2 where we go through some more advanced conversions
including multiple unit conversions.
If you don't get it, rewind the video and review this concept again and again until
the concept of given times ratio so that the ratio cancels clicks because once you get
it everything becomes so much easier.
You can find additional MCAT Chemistry videos on my website leah4sci.com/Chemistry and if
you still have trouble doing Math without a calculator, remember you can't use a calculator
on the MCAT.
Simply visit leah4sci.com/MCATMath where I take you through all the different concepts
in Math that you have to do on the MCAT and I show you tricks and shortcuts for how to
do them without a calculator.
The link again, leah4sci.com/MCATMath.