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
Top Related