Unit conversion within the metric system Metric unit conversion
Unit conversion within the metric system
- 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!
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