SOLUTION: I have been having trouble with unit multipliers, and my algebra teacher isn't very good at explaining them. I have missed them on every test. I had a test today, and it was wrong.

Algebra ->  Conversion and Units of Measurement -> SOLUTION: I have been having trouble with unit multipliers, and my algebra teacher isn't very good at explaining them. I have missed them on every test. I had a test today, and it was wrong.      Log On


   

Question 164517: I have been having trouble with unit multipliers, and my algebra teacher isn't very good at explaining them. I have missed them on every test. I had a test today, and it was wrong.
Here is the problem:
Convert 710m. to inches. (Go from m to cm to in)
On the test I tried something like:
(the dashes represent spaces in between fractions)
-----1000cm.----1m.-----71000cm.----1in.---------71000(2.54)in
710•_____x______=_________x_________=________________
-----1m.--1000cm.----1------2.54cm.----------1

i would just simply like to know:
(in words) how to do a unit multiplier
and how to do the test question above.
thank you.
Found 2 solutions by josmiceli, Edwin McCravy:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
I can only tell you how I do it. I had a very good teacher in
high school demonstrate it, and it stuck pretty good in
college.
The best way to learn is do do REALLY long coversions.
Convert cm/sec to miles/hr
OK-I've got to get rid of that cm on top
I can do it like this:
(cm)(miles/cm)
Stop and think- Why can I do this? The only way I can do it
and not change what I started out with is if the (cm/mile)=1,
then (cm)x1 = (cm).
So, as long as I have calculated the EXACT number of cm in 1 mile
or the EXACT fraction of a mile in 1 cm, then I am doing (cm)x1 = (cm)
OK
(cm)(miles/cm) = miles because the cm on top cancels with the
one on the bottom.But what if I don't know the conversion (miles/cm)?
Maybe I should try (meters/cm)
(cm)(meters/cm) = meters. But I want miles. I've got more work to do
(cm)(meters/cm)(miles/meter) = miles
Can you see that cm on top and bottom are the same as (cm/cm)
and meters on top and bottom are the same as (meters/meters)?
Again, what if I don't know the conversion (miles/meter)?
What if I only know (feet/meter)? Then I can do:
(cm)(meters/cm)(feet/meter)(miles/feet) = miles
You can look at it like this:
(cm/cm)(meters/meters)(feet/feet)(miles)
I'm left with miles which is what I want, but
it only works if my conversions are EXACTLY correct
How many miles are in 1 foot?
A very small fraction of a mile: 1%2F5280miles to be exact
How many feet are in a meter? Around 3, but you can look it up.
If you get the idea of units cancelling on the top
and bottom, you're OK. Keep practicing long conversions to get it
right. Remember if somewhere you say (11 inches/1 foot), you'll
be wrong even if your units are correct

Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!
EDWIN'S SOLUTION:
Convert 710m. to inches. (Go from m to cm to in) 

     Start by putting 710m over 1:

710m%2F1

     Now we want to cancel away the m and bring in
     cm.  We know that 1m=100cm.  So there are
     two possible unit multipliers which we can make with
     that.  We can make the unit multiplier %281m%29%2F%28100cm%29
     or the unit multiplier %28100cm%29%2F%281m%29.  The question
     is which one do we make.  Since we have m in the
     numerator, we must use the unit multiplier which has
     m in the denominator so the m's will cancel.
     So we multiply by %28100cm%29%2F%281m%29.  

matrix%281%2C3%2C710m%2F1%2C+%22%D7%22%2C%28100cm%29%2F%281m%29%29+ 

     and then the m's cancel, like this

matrix%281%2C3%2C710cross%28m%29%2F1%2C+%22%D7%22%2C%28100cm%29%2F%281cross%28m%29%29%29+


     Now we want to cancel away the cm and bring in
     in.  We know that 1in=2.54cm.  So there are
     two possible unit multipliers which we can make with
     that.  We can make the unit multiplier %281in%29%2F%282.54cm%29
     or the unit multiplier %282.54cm%29%2F%281in%29.  The question
     is which one do we make.  Since we have cm in the
     numerator, we must use the unit multiplier which has
     cm in the denominator so the cm's will cancel.
     So we multiply by %281in%29%2F%282.54cm%29.  


 
     Then the cm's cancel:



     So we have left:



     Multiply the numerators and the denominators:

%28710%2A100%2A1in%29%2F%281%2A1%2A2.54%29

%2871000in%29%2F%282.54%29

matrix%281%2C2%2C71000%2F2.54%2Cin%29

matrix%281%2C2%2C27952.75591%2Cin%29

     You probably should round that off. Ask your teacher 
     how he or she wants it rounded.

     Edwin