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Welcome to the[br]presentation on units.

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Let's get started.

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

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0.05 kilometers-- some[br]people say KIL-ometers

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or kil-O-meters.

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If I have traveled 0.05[br]kilometers, how many

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centimeters have I traveled?

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That's question[br]mark centimeters.

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

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know what these prefixes[br]centi and kilo mean.

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

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

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of paper, just so you[br]have a reference.

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So kilo means 1,000, hecto[br]means 100, deca means 10.

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You might recognize that[br]from decade, 10 years.

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And then, of course, you[br]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[br]between cases.

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centi is equal to[br]0.01, or 1/100.

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And then milli is equal[br]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,[br]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[br]millipede has 1,000 feet, but

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that's the implication when[br]someone says a millipede

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because pede means feet.

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So let's go back[br]to the problem.

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If I have 0.05 kilometers, how[br]many centimeters do I have?

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Whenever I do a problem like[br]this, I like to actually

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convert my number to[br]meters because that's

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very easy for me.

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

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we can abbreviate this[br]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[br]into meters, is it going to be

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more than 0.05 meters[br]or less than 0.05?

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Well, a kilometer is a very[br]large distance, so in terms

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

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So we can multiply this times[br]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[br]is equal to 50, right?

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I just multiplied[br]0.05 times 1,000.

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And with the units, I now[br]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[br]with this, you can treat units

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exactly the same way that you[br]would treat numbers

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or variables.

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As long as you have the same[br]unit in the numerator and the

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denominator, you can cancel[br]them out, assuming that you're

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not adding units, you're[br]multiplying units.

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So you have kilometers times[br]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[br]reality check after every step.

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

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

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number 1,000, because that's[br]the relationship between

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a kilometer and a meter.

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And you're always confused,[br]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,[br]well, if I'm going from

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

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1,000 meters, right?

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

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I'm going to get[br]a bigger number.

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So that's why I went from[br]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[br]to the problem.

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0.05 kilometers is[br]equal to 50 meters.

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We're not done yet.

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

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Well, we do the same thing.

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

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meters and centimeters?

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

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

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by 100, or am I going[br]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[br]to a smaller unit, so one of

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

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So we're going to multiply.

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So we say times 100[br]centimeters per meter, right?

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And that just makes sense.

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There's 100 centimeters[br]per meter.

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So 50 meters times 100[br]centimeters per meter is equal

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

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and you get centimeters.

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So what we have here is that[br]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[br]you see, it'll make them

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a little more sense.

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

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Otherwise, it's very[br]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[br]a very small amount.

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

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system, they measure[br]gold in terms of grams.

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And I want to convert[br]this into milligrams.

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

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Am I going from a bigger unit[br]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[br]of a gram, and I'm going

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to 1/1,000 of a gram.

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[br]So there's two ways[br]of doing this.

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We can convert to grams and[br]then convert to the other unit.

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That sometimes[br]make things easy.

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Or we could say, well,[br]how many milligrams is

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equal to one decigram?

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Well, a milligram, as[br]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,[br]you have to decrease

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in size by 100.

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So we could just say 422[br]decigrams times 100

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milligrams per decigram.

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

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times 100, 42,200 milligrams.

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[br]Now, another way you could have[br]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[br]could convert that to grams.

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

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That's not really a[br]familiar unit-- decigrams.

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And how many decigrams[br]are there per gram?

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

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number of grams, right?

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So we could say times[br]1 decigram is equal

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to how many grams?

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Well, 1 decigram is[br]equal to-- no, sorry.

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1 gram is equal to[br]how many decigrams?

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Well, 1 gram is equal[br]to 10 decigrams.

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

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in the numerator here, we want[br]a decigram in the

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denominator here.

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

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that divided by 10 is[br]equal to 42.2 grams.

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And now we can just go[br]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[br]milligrams, so we could say

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times 1,000 milligram per gram.

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The grams cancel out, and[br]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[br]confuse you too much.

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The important thing is to[br]always take a step back and

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really visualize and think[br]about, should I be getting a

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larger number or a smaller[br]number than the one

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I started off with?

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

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Have fun!