>> Welcome to a video tutorial to help you
with converting between metric units.
Let's begin.
So I'm going to share with you two different approaches
to converting between metric units.
The first way is the way commonly used by chemists
where we would use conversion factors.
So for example, if we wanted to convert between milligrams
and grams, we can use the metric conversion
that there are 1,000 milligrams equals 1 gram.
Or we could say that 1 milligram is 10 to the minus 3 grams.
So whichever way you're comfortable defining the
relationship between metric units.
Use whichever term you feel is the best.
So how many milligrams are in this many grams?
So we have .53 grams and we go-- there's--
for every gram we have 1,000 milligrams, right.
Or we start with the same--
the same way but I'll do it the other way.
There's 10 to the minus 3 grams in every milligram.
Notice that it doesn't matter
which way you set up the calculation.
When you plug in the values,
we're going to get the same result.
So let me punch that into my calculator here.
OK. So either way we're going to have 530 milligrams.
And because we are working within the metric system,
the sig figs will never change.
If we have two sig figs to start, this is defined
so it has infinite sig figs or you could think of it as exact.
So our final result should have two sig figs.
Now the other way to approach metric conversions is the
shifting method.
Now the shifting method requires a little bit of memorization,
but once you have the set up it can be very handy.
So we need to look at the metric prefixes in the following order.
So it only works if we write them this way.
So we start with kilo on the left and then 10 to the 0,
that would be our base unit.
10 to the minus 1 is deci; 10 to the minus 2, centi;
10 to the minus 3, milli; and then we'll jump up to 10
to the minus 6 is micro.
All right.
So now we can take advantage of the fact
that we can shift the decimal by adding
or subtracting the exponential terms.
All right.
So let me give you-- let's do some examples
to let me show you how this works.
All right.
How many decigrams are in 3,475,892 micrograms?
So notice we're starting here at micrograms
and we want to go to decigrams.
All right.
So we are going to move here.
So we're moving from minus 6 to minus 1.
So we're going to go five, right, five to the left.
We're going to shift our decimal.
All right.
So let's write this out.
So right now the decimal is here.
So we have to shift it five to the left.
One, two, three, four, five.
All right.
So we would rewrite the value.
This would become 34.75892 decigrams.
So there is the shifting method.
Let me demonstrate it for you one more time.
All right.
Here is an example where we have kiloliters.
So now we're over here at kiloliters and we want
to shift to milliliters.
So this time we're going to go to the right.
All right.
So to go from kiloliters to milliliters, all right,
3 and then minus 3 so that would be six units
so that's a shift of six.
So if we have-- if the decimal started here,
we're going to shift six to the right.
So one, two, three, four, five, six.
Our decimal goes right there.
So we're going to have to add 0's.
All right.
So that would be 375,000 milliliters.
All right.
So one method is not superior to the other.
It's whatever feels most comfortable to you.
I think the idea though for those
of you entering allied health careers, is you want to get
to where you can shift back and forth.
And these are the primary metric units
that you'll be using in your profession.
There are many more metric prefixes out there,
but you're not going to need to worry about those.
All right.
So now with unit conversions, let's take our metric units
and convert them into English units because we live
in a country that still uses the English unit system.
So in this case, it's important to have bridges.
And so the bridges are linked to the main descriptions of matter.
Right. So everything with matter has mass and volume.
And then it can be helpful to also have a distance conversion.
And so I will share with you my favorite bridges,
but you can have your own bridges.
So for me, 453.6 grams equals 1 pound.
When I'm looking at a mass conversion from the metric
to the English system, this is the conversion
that pops into my brain.
If you have another one, that's fine.
Volume. So when we're converting between volumes, I like to go
from liters to quarts.
And so let me pull up that one.
So for every liter we have 1.057 quarts.
And then for distance, I like to use 2.54 centimeters in an inch.
So it doesn't matter which bridges you pick.
It just matters that you have bridges.
And you need at least three bridges, one for mass,
one for volume, and one for distance.
So let's practice using our bridges.
What is the kilogram weight of a 210 pound patient?
This is a very common conversion.
So we start with the weight of the patient in pounds
and then here, my bridge is not necessarily the best bridge.
We have 1 pound, 453.6 grams.
And then we're trying to get to kilograms so then we would have
to say that there are 1,000 grams in a kilogram.
So some of you might have gone, well,
there's a easier way to do that.
And there is.
So let's go that way too.
We could go directly from pounds to kilograms
because there are 2.205 pounds in every kilogram.
So I've shown the calculation two ways.
And in my dream world that will be empowering to you
because notice that it doesn't matter
which way we solve the problem.
If we go from pounds to grams and grams to kilograms
or if we quickly just go straight from pounds
to kilograms, regardless of the way we set it up,
the final units are in kilograms and so the final answer is going
to be the same either way.
So I'll punch the values in for the first calculation and we see
that this patient weighs 95.26 kilograms.
Or if we use the alternate method,
we see that we get 95.24 kilograms but now let's bring
in our sig figs and so for both--
in both cases we would report two sig figs.
And so notice that when we go
to two sig figs we get the exact result, 95 kilograms.
So hopefully this is empowering to you
that there's no magic formula.
No special way.
That as long
as we systematically apply our conversions we can get the
correct answer.
Let's practice one more.
A typical member of the species Vibrio cholerae is 8.8 times 10
to the minus 6 meters long.
How long is this in inches?
All right.
So now we're going to take advantage
of our distance bridge.
So start with what we know.
We know we have 8.8 times 10 to the minus 6 meters.
Well, and so for every meter we would have 100 centimeters.
And then for every 2.54 centimeters, 1 inch.
So if we look at our units here, the meters cancel
and the centimeters cancel and we're left with inches,
which is what the question is asking for.
So now we can punch this into our calculator and so entering--
there is a scientific notation tutorial that can help you
if you're unsure about how
to do scientific notation in your calculations.
All right.
And then the calculator spits
out a very small number, .000346 inches.
And, last but not least, we have two sig figs here.
This is infinite sig figs.
It's exact because it's defined.
And then here we have three sig figs so for our final answer,
remember leading 0's never count.
So it would be 0.0035 inches for that bacteria.
All right.
So now let's go to some more challenging conversions
to build our confidence.
All right.
So now we're going to need several conversion factors.
Horse racing uses the distance of furlongs.
If a mile is defined as 8 furlongs,
how many kilometers is a 22 furlong race?
All right.
So we know that 1 mile equals 8 furlongs.
OK. And it's important with miles, write mi.
Make sure the pay attention to the difference
between miles and meters.
And we want to get to kilometers.
That's what we're curious about.
And so where do we start?
We start here.
OK. So we have a 22 furlong race.
And we're trying to get to kilometers.
So because we have our bridges, we know that we can get
from miles to kilometers.
And so the first thing we do is we have to get
out of these crazy furlongs and get into miles.
And then by now everyone should have memorized that there--
in every mile there are 1.609 kilometers.
So we did our first conversion to get- convert out of furlong
into miles and then we could go from miles to kilometers.
And then we have the units that the question asks
for so we can go ahead and punch our result into the calculator.
And we would see that this would be a 4.425 kilometer race.
And, last but not least, let's check our sig figs.
So we have two sig figs here.
This is exact because it's defined
so it has infinite sig figs.
And then we have four sig figs.
So this race would be a 4.4 kilometer race.
All right.
So we haven't worked with volume too much yet.
Let's practice.
We'll do one more practice problem
and practice with volume.
So there are 42 gallons in 1 barrel of crude oil.
How many milliliters of crude oil are contained in 1 barrel?
All right.
So this is taking advantage of the English system.
So you need to know that there are 4 quarts in 1 gallon.
And then that links us to our bridge
because there are 1.057 quarts in a liter.
And so-- and we're asked to get to milliliters.
And then we know there are 1,000 milliliters in a liter.
So it's a good problem solving strategy to--
when you look at a question, look at the gallons.
Look at the units we're given
and the units we're asked to solve for.
And just start brainstorming all
of the different possible conversions that you may need.
It can be really helpful to write those on the paper.
And so then as we go to solve it, we have that information.
And ideally, all of this information will start
to be second nature in your brain.
So we start here with-- we have a 42 gallon barrel of oil.
And we're trying to get to milliliters.
So since we have a bridge here from quarts to liters,
I'm going to go ahead and take advantage of the fact
that 1 gallon is defined.
All right.
So this is defined in the English system to 4 quarts.
Then we can use our bridge, 1.057 quarts in a liter.
And then, last but not least,
in a liter there are 1,000 milliliters.
So we used an English unit conversion to go
from gallons to quarts.
We used one of our metric, English bridges to get
from English to metric volume.
And then we used a metric conversion to get
to milliliters, which the question asked us to solve for.
So now that our units get--
let us know that we've done a correct set up, we can go ahead
and plug the numbers into our calculator.
OK. And we find out that this a huge number, 158940 milliliters.
So there's the display from the calculator.
And then, last but not least, let's go ahead
and report this using the correct number of sig figs.
So two sig figs here, infinite, infinite, and four.
So we would report this answer to two sig figs.
Sometimes this feels really strange,
but it would be 160,000 milliliters.
So that concludes our conversion tutorial emphasizing metric
units, metric-to-metric conversions,
and metric-to-English.
So go ahead now and practice a few more problems like this
from your homework and to reinforce your understanding.