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Welcome to the
presentation on units.
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Let's get started.
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So if I were to ask you, or if
I were to say, I have traveled
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0.05 kilometers-- some
people say KIL-ometers
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or kil-O-meters.
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If I have traveled 0.05
kilometers, how many
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centimeters have I traveled?
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That's question
mark centimeters.
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So before we break into the
math, it's important to just
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know what these prefixes
centi and kilo mean.
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And it's good to memorize this,
or when you're first starting
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to do these problems, you can
just write them down on a piece
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of paper, just so you
have a reference.
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So kilo means 1,000, hecto
means 100, deca means 10.
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You might recognize that
from decade, 10 years.
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And then, of course, you
have no prefix, means 1.
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No prefix.
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No prefix equals 1.
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deci is equal to 0.1 or 1/10.
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centi-- I keep changing
between cases.
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centi is equal to
0.01, or 1/100.
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And then milli is equal
to 0.001, and that's the
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same thing as 1/1,000.
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And the way I remember, I mean,
centi, if you think of a
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centipede, it has a 100 feet.
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A millipede, I'm not sure if a
millipede has 1,000 feet, but
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that's the implication when
someone says a millipede
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because pede means feet.
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So let's go back
to the problem.
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If I have 0.05 kilometers, how
many centimeters do I have?
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Whenever I do a problem like
this, I like to actually
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convert my number to
meters because that's
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very easy for me.
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And actually, I'm going to
abbreviate this is km, and
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we can abbreviate this
as cm for centimeters.
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So let's say 0.05 km.
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Well, if I want to convert this
into meters, is it going to be
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more than 0.05 meters
or less than 0.05?
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Well, a kilometer is a very
large distance, so in terms
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of meters, it's going to
be a much bigger number.
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So we can multiply this times
1,000 meters, and I'll do
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it over 1, per kilometer.
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And what does that get?
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Well, 0.05 times 1,000
is equal to 50, right?
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I just multiplied
0.05 times 1,000.
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And with the units, I now
have kilometers times
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meters over kilometers.
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And the kilometers cancel out.
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And just so you're familiar
with this, you can treat units
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exactly the same way that you
would treat numbers
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or variables.
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As long as you have the same
unit in the numerator and the
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denominator, you can cancel
them out, assuming that you're
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not adding units, you're
multiplying units.
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So you have kilometers times
meters divided by kilometers,
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and that equals 50 meters.
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And it's good to always do a
reality check after every step.
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Usually when you do these types
of problems, you know, OK, if I
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want to go from kilometers to
meters, I'm going to use the
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number 1,000, because that's
the relationship between
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a kilometer and a meter.
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And you're always confused,
well, do I multiply by 1,000,
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or do I divide by 1,000?
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And you always have to say,
well, if I'm going from
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kilometers to meters, I'm
going-- 1 kilometer is
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1,000 meters, right?
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So I'm going to be
multiplying by 1,000.
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I'm going to get
a bigger number.
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So that's why I went from
0.05, and I multiplied it
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by 1,000, and I got 50.
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So let's get back
to the problem.
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0.05 kilometers is
equal to 50 meters.
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We're not done yet.
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Now, you need to convert those
50 meters into centimeters.
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Well, we do the same thing.
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50 meters times-- how many-- so
what's the relationship between
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meters and centimeters?
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Well, if we look at the
chart, we see it's 100.
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And the question I'm going to
ask you, am I going to multiply
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by 100, or am I going
to divide by 100?
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Well, it's the same thing.
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We're going from a bigger unit
to a smaller unit, so one of
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a bigger unit is equal to a
bunch of the smaller units.
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So we're going to multiply.
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So we say times 100
centimeters per meter, right?
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And that just makes sense.
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There's 100 centimeters
per meter.
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So 50 meters times 100
centimeters per meter is equal
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to 50 times 100 is 5,000, and
then the meters cancel out,
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and you get centimeters.
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So what we have here is that
0.05 kilometers is equal
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to 5,000 centimeters.
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Let's do another problem.
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I think the more examples
you see, it'll make them
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a little more sense.
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And always try to visualize
what we're doing, the scale.
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Otherwise, it's very
confusing whether you
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should multiply or divide.
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Let's say I have 422 decigrams.
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Grams are a measure of mass.
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One gram is actually
a very small amount.
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That's what you measure--
I guess in the metric
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system, they measure
gold in terms of grams.
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And I want to convert
this into milligrams.
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So before we start the problem,
let's just do a reality check.
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Am I going from a bigger unit
to a smaller unit, or a smaller
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unit to a bigger unit?
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Well, decigrams, that's 1/10
of a gram, and I'm going
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to 1/1,000 of a gram.
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So there's two ways
of doing this.
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We can convert to grams and
then convert to the other unit.
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That sometimes
make things easy.
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Or we could say, well,
how many milligrams is
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equal to one decigram?
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Well, a milligram, as
we see here, is 100
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times smaller, right?
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To go from 1/10 to 1/1,000,
you have to decrease
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in size by 100.
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So we could just say 422
decigrams times 100
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milligrams per decigram.
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And then the decigrams will
cancel out, and I'll get 422
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times 100, 42,200 milligrams.
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Now, another way you could have
done it is the way we just
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did that last problem.
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We could say 422 decigrams, we
could convert that to grams.
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We could say 422-- I'm
just going to say dg.
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That's not really a
familiar unit-- decigrams.
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And how many decigrams
are there per gram?
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If we're going to gram, 422
is going to be a smaller
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number of grams, right?
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So we could say times
1 decigram is equal
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to how many grams?
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Well, 1 decigram is
equal to-- no, sorry.
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1 gram is equal to
how many decigrams?
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Well, 1 gram is equal
to 10 decigrams.
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And the reason why this makes
sense is if we have a decigram
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in the numerator here, we want
a decigram in the
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denominator here.
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So if we have decigrams cancel
out, 422 decigrams will equal--
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that divided by 10 is
equal to 42.2 grams.
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And now we can just go
from grams to milligrams.
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Well, that's an easy one.
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1 gram is equal to 1,000
milligrams, so we could say
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times 1,000 milligram per gram.
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The grams cancel out, and
we're left with 42,200
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milligrams, right?
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42.2 times 1,000.
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Hopefully, that doesn't
confuse you too much.
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The important thing is to
always take a step back and
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really visualize and think
about, should I be getting a
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larger number or a smaller
number than the one
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I started off with?
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I think you're ready to
now try some problems.
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Have fun!