Question

Set up and solve the following using dimensional analysis.

Answer 1

1).  Multiply (5400 inches) by (1 foot / 12 inch) then by (1 mile / 5280 foot).

      (See explanation at the bottom)

         =      (5400 inch) x (1 foot / 12 inch) x (1 mile / 5280 foot)

         =      (5400 x 1 x 1 / 12 x 5280)  (inch - foot - mile / inch - foot) 

         =          0.0852  mile  


2).  Multiply (16 week) by (7 day/week) then by (24 hour/day)
       then by (60 minute/hour) then by (60 sec/minute).

3).  Multiply (54 yards) by (3 foot/yard) then by (1 meter/3.28 foot)
       and then by (1000 mm/meter)

4).  Multiply (36 cm/second) by (3600 second/hour) then by (1 meter/100 cm)
      then by (1 mile/1609.3 meter).

5).  Look up how many grams in a pound  ('P')
       Look up how many mL in a gallon       ('G')

      Multiply (1.09 g/mL) by ( 1 pound/ P gram) then by (1 gallon/ G mL)

6).  Multiply (32 foot/sec) by (1 meter / 3.28 foot) then by (60 sec/minute).


Each time I told you to multiply by something, it was always a fraction
where the numerator and denominator are equal, like (60 seconds/minute)
or (1 foot / 12 inch).  Since the top and bottom of the fraction are equal, the
value of the fraction is ' 1 ' , and multiplying by it doesn't change the value,
it only changes the units ... that's what this whole exercise is about.
When you multiply, KEEP the units in the product, and then, after you multiply, you can 'cancel' units out of the top and bottom of the product.
Like if you have 'feet' on top and bottom, just cross them out.  When you're done, if you did it correctly, the last unit you end up with will be the one you want.