Conversions

Not the religious kinds, either

Why Why Why?

• Why do we do conversions?– teachers are mean

• not entirely

– really for real world value• cooking

– how many cups in a quart

• trip to Paris– miles per hour to kilometers per hour

• How do we do conversions?– number line– dimensional analysis

The Conga Number Line• If we use the number line, it goes

something like this:– count the number of spaces from one unit

to the other– move your decimal the same number of

places, in the same direction– The number line looks like this:

M - - k - - base - c m - - - - n

The players

• M = Mega

• k = kilo

• base = base units

• c = centi

• m = milli = micro

• n = nano

• NOTE: c m (below) is not centimeters!

M - - k - - base - c m - - - - n

Da da da da da, dun• Let’s convert 4000 km to m

– That’s kilometers to meter– Base unit is . . .

• the meter

• 1st, we find the unit we coming from– k

• Next, we find where we’re going– base

• Count the spaces between, noting the direction

M - - k - - base - c m - - - - n

1 23

Start

Conga!

• So we went 3 spaces, to the right

• Move your decimal three places to the right

• You will find:

4000. km = 4000000 m

•But what do we do?

•fill in the blanks with zeros!

But the fat lady isn’t singing

• What if we want to convert km to miles?– or days to hours or to minutes

• Number line is a sophomoric method, we use dimensional analysis

• I would bet you already do this, but don’t realize it!– If you can tell me how many hours are in three

days, you can!

That’s a fancy word Mr. Bitzer• Relax, it’ll be okay. We’ll start with an

easy one• How many hours are in 3 days?• First, we need to know how days and

hours are related– Hopefully, we know that there are 24 hours

in a day– If we write this using math,

24 hours = 1 day• this is called a unity conversion, because

something = 1

Wait a minute!

• So we know that 1 day = 24 hours; we want to know how many hours are in 3 days

• but we just multiply 3*24 = 72; that’s easy!• How’d you know to do that?

• Let’s set it up:

3 days? hrs

What we’re trying to convert What we’re converting to

Our unity conversion goes here

1 day

24 hr

But what goes where?

• We know we use 1 day = 24 hour, but how?• We want days to cancel, and be left with hours• Let’s try it

3 days? hrs

Does anything cancel?NO!

Uh oh :-( Try it the other way now!

24 hr

1 day

So the days cancel, and we’re left with hours

Now we simply do what the fraction tells us

If we had a number on the bottom, we would simply divide

The answer:

• I know it seems like this is a hard way now, but it’s much easier once you get the hang of it

• When using the metric system, you should know the exponents from the beginning of the year (pg 17 in your book)

3*24 / 1 = 72 hrs3 days 24 hr

1 day

Powers that be

• nano = 10-9

• micro = 10-6

• milli = 10-3

• centi = 10-2

• kilo = 103

• Mega = 106

• We should know these, but if not, know is a good time to learn.

• We use these by saying 1 cm = 10-2 m

• Or we say 1 kg = 103 g• Replace the prefix with the

appropriate power1 Mm =1 mega meter =

106 m

Back to our original example

• We’re converting 4000 km to meters

• We know 1 km = 103 m

• Again, set it up so the units cancel

• This isn’t right!

4000 km? m

What we’re trying to convert What we’re converting to

Our conversion goes here

4000 km = ? m

1 km

103 m

Try number two:

• This is right!• The km cancel

• We’re left with m– this is what we want

• See this is the same thing as before!

4000 km4000 x 103 m

What we’re trying to convert What we’re converting to

Our conversion goes here

4000 km = ? m

1 km

103 m

Conversions

• This is the way that we will do conversions

• There is no way to forget the number line

• The only thing to remember are those 7 prefixes from the previous slide

One last example . . .

• Let’s convert 4000 g to kg– We’re starting from

• grams (the base)

– We’re going to • kilo

• Set it up yourself:

You should have:

• You would divide 4000 by 103 and you will get . . .

4000 g 1 kg

103 g4 m

Not just for simple conversions

• We can also convert 100 km/hr to m/sec• first convert km to m, then hr to sec

100 km

hr 1 km

103 m 1 hr

60 min

1 min

60 sec

100* 103 m

60*60 sec

100000 m

3600 sec

27.78 m/sec

Works for any conversion

• Now we can handle conversion such as kilometers to miles, if we know the unity conversion– 1 mi = 1.61 km

• Or pounds to Newtons– 1 lb = 4.45 N

– remember, pound is not a measurement of mass!

• Or inches to cm– 1 in = 2.54 cm

Convert everything you can• Go forth and multiply

– or divide

• Go door to door, trying to convert people or things

• If there are questions, tutoring is available thru MAO, NHS, or Mr. Bitzer– MAO = Wednesdays second half– NHS = Tuesdays second half– Mr. Bitzer = Monday, Wednesday mornings