Welcome to the
presentation on units.

Let's get started.

So if I were to ask you, or if
I were to say, I have traveled

0.05 kilometers-- some
people say KIL-ometers

or kil-O-meters.

If I have traveled 0.05
kilometers, how many

centimeters have I traveled?

That's question
mark centimeters.

So before we break into the
math, it's important to just

know what these prefixes
centi and kilo mean.

And it's good to memorize this,
or when you're first starting

to do these problems, you can
just write them down on a piece

of paper, just so you
have a reference.

So kilo means 1,000, hecto
means 100, deca means 10.

You might recognize that
from decade, 10 years.

And then, of course, you
have no prefix, means 1.

No prefix.

No prefix equals 1.

deci is equal to 0.1 or 1/10.

centi-- I keep changing
between cases.

centi is equal to
0.01, or 1/100.

And then milli is equal
to 0.001, and that's the

same thing as 1/1,000.

And the way I remember, I mean,
centi, if you think of a

centipede, it has a 100 feet.

A millipede, I'm not sure if a
millipede has 1,000 feet, but

that's the implication when
someone says a millipede

because pede means feet.

So let's go back
to the problem.

If I have 0.05 kilometers, how
many centimeters do I have?

Whenever I do a problem like
this, I like to actually

convert my number to
meters because that's

very easy for me.

And actually, I'm going to
abbreviate this is km, and

we can abbreviate this
as cm for centimeters.

So let's say 0.05 km.

Well, if I want to convert this
into meters, is it going to be

more than 0.05 meters
or less than 0.05?

Well, a kilometer is a very
large distance, so in terms

of meters, it's going to
be a much bigger number.

So we can multiply this times
1,000 meters, and I'll do

it over 1, per kilometer.

And what does that get?

Well, 0.05 times 1,000
is equal to 50, right?

I just multiplied
0.05 times 1,000.

And with the units, I now
have kilometers times

meters over kilometers.

And the kilometers cancel out.

And just so you're familiar
with this, you can treat units

exactly the same way that you
would treat numbers

or variables.

As long as you have the same
unit in the numerator and the

denominator, you can cancel
them out, assuming that you're

not adding units, you're
multiplying units.

So you have kilometers times
meters divided by kilometers,

and that equals 50 meters.

And it's good to always do a
reality check after every step.

Usually when you do these types
of problems, you know, OK, if I

want to go from kilometers to
meters, I'm going to use the

number 1,000, because that's
the relationship between

a kilometer and a meter.

And you're always confused,
well, do I multiply by 1,000,

or do I divide by 1,000?

And you always have to say,
well, if I'm going from

kilometers to meters, I'm
going-- 1 kilometer is

1,000 meters, right?

So I'm going to be
multiplying by 1,000.

I'm going to get
a bigger number.

So that's why I went from
0.05, and I multiplied it

by 1,000, and I got 50.

So let's get back
to the problem.

0.05 kilometers is
equal to 50 meters.

We're not done yet.

Now, you need to convert those
50 meters into centimeters.

Well, we do the same thing.

50 meters times-- how many-- so
what's the relationship between

meters and centimeters?

Well, if we look at the
chart, we see it's 100.

And the question I'm going to
ask you, am I going to multiply

by 100, or am I going
to divide by 100?

Well, it's the same thing.

We're going from a bigger unit
to a smaller unit, so one of

a bigger unit is equal to a
bunch of the smaller units.

So we're going to multiply.

So we say times 100
centimeters per meter, right?

And that just makes sense.

There's 100 centimeters
per meter.

So 50 meters times 100
centimeters per meter is equal

to 50 times 100 is 5,000, and
then the meters cancel out,

and you get centimeters.

So what we have here is that
0.05 kilometers is equal

to 5,000 centimeters.

Let's do another problem.

I think the more examples
you see, it'll make them

a little more sense.

And always try to visualize
what we're doing, the scale.

Otherwise, it's very
confusing whether you

should multiply or divide.

Let's say I have 422 decigrams.

Grams are a measure of mass.

One gram is actually
a very small amount.

That's what you measure--
I guess in the metric

system, they measure
gold in terms of grams.

And I want to convert
this into milligrams.

So before we start the problem,
let's just do a reality check.

Am I going from a bigger unit
to a smaller unit, or a smaller

unit to a bigger unit?

Well, decigrams, that's 1/10
of a gram, and I'm going

to 1/1,000 of a gram.

So there's two ways
of doing this.

We can convert to grams and
then convert to the other unit.

That sometimes
make things easy.

Or we could say, well,
how many milligrams is

equal to one decigram?

Well, a milligram, as
we see here, is 100

times smaller, right?

To go from 1/10 to 1/1,000,
you have to decrease

in size by 100.

So we could just say 422
decigrams times 100

milligrams per decigram.

And then the decigrams will
cancel out, and I'll get 422

times 100, 42,200 milligrams.

Now, another way you could have
done it is the way we just

did that last problem.

We could say 422 decigrams, we
could convert that to grams.

We could say 422-- I'm
just going to say dg.

That's not really a
familiar unit-- decigrams.

And how many decigrams
are there per gram?

If we're going to gram, 422
is going to be a smaller

number of grams, right?

So we could say times
1 decigram is equal

to how many grams?

Well, 1 decigram is
equal to-- no, sorry.

1 gram is equal to
how many decigrams?

Well, 1 gram is equal
to 10 decigrams.

And the reason why this makes
sense is if we have a decigram

in the numerator here, we want
a decigram in the

denominator here.

So if we have decigrams cancel
out, 422 decigrams will equal--

that divided by 10 is
equal to 42.2 grams.

And now we can just go
from grams to milligrams.

Well, that's an easy one.

1 gram is equal to 1,000
milligrams, so we could say

times 1,000 milligram per gram.

The grams cancel out, and
we're left with 42,200

milligrams, right?

42.2 times 1,000.

Hopefully, that doesn't
confuse you too much.

The important thing is to
always take a step back and

really visualize and think
about, should I be getting a

larger number or a smaller
number than the one

I started off with?

I think you're ready to
now try some problems.

Have fun!