1. Not the religious kinds, either
Conversions
Not the religious kinds, either

2. Why Why Why? Why do we do conversions? How 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

3. The Conga Number Line M - - k - - base - c m - -  - - n
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

4. The players M - - k - - base - c m - -  - - n 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

5. Da da da da da, dun M - - k - - base - c m - -  - - n
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 1 2 3
Start
M - - k - - base - c m - -  - - n

6. Conga! 4000. km = 4000000 m So we went 3 spaces, to the right
Move your decimal three places to the right
You will find:
km = m
But what do we do?
fill in the blanks with zeros!

7. 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!

8. 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

9. 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:
Our unity conversion goes here
3 days
? hrs
What we’re trying to convert
What we’re converting to

10. But what goes where? 3 days ? hrs 1 day 24 hr 24 hr 1 day
We know we use 1 day = 24 hour, but how?
We want days to cancel, and be left with hours
Let’s try it
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
Does anything cancel?
NO!
Uh oh :-(
Try it the other way now!

11. The answer:
3 days
24 hr
1 day
3*24 / 1 = 72 hrs
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)

12. 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 power
1 Mm =1 mega meter = m

13. Back to our original example
Our conversion goes here
4000 km = ? m
4000 km
1 km
? m
What we’re trying to convert
103 m
What we’re converting to
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!

14. Try number two: This is right! The km cancel Our conversion goes here
4000 km = ? m
4000 km
1 km
103 m
4000 x 103 m
What we’re trying to convert
What we’re converting to
This is right!
The km cancel
We’re left with m
this is what we want
See this is the same thing as before!

15. 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

16. One last example . . . Let’s convert 4000 g to kg Set it up yourself:
We’re starting from
grams (the base)
We’re going to
kilo
Set it up yourself:

17. You should have: You would divide 4000 by 103 and you will get . . .
1 kg
103 g
4 m
You would divide 4000 by 103 and you will get . . .

18. Not just for simple conversions
We can also convert 100 km/hr to m/sec
first convert km to m, then hr to sec
1 km
103 m
100 km hr
1 hr
60 min
1 min
60 sec
100* 103 m
60*60 sec m
3600 sec
27.78 m/sec

19. 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

20. 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