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Conversions

Sometimes conversions seem troublesome, they do get easier with practice (like most things). If your notes are not handy review the example below.

Sample conversion

You just bought a 25 lb watermelon. It is 92% water. How many grams of water have you just purchased?

Conversion factors:

Watermelon = 92% water ( 1 lb melon = 0.92 lb water contained); 1kg = 2.2 lbs; 1000 g = 1 kg; 

  1. Start with the known variable. Place it in the 1st box with its unit label
  2. Place other conversion factors so they will cancel the previous units.

 25 lb melon  0.92 lb water  1 kg water  1000 g water
   1 lb melon  2.2 lb water  1 kg water

If melon is on top in the first box you want in below in the second set of boxes. The relationship that has melon in it is 1 lb melon would give 0.92 lbs water. That is the meaning of 92% water.

 25 lb melon  0.92 lb water  1 kg water  1000 g water
   1 lb melon  2.2 lb water  1 kg water

Then continue cancel lbs of water on top with a relationship (conversion factor) with lbs in it. That relationship is 2.2 lbs equals 1 kg. Now these units cancel

 25 lb melon  0.92 lb water  1 kg water  1000 g water
   1 lb melon  2.2 lb water  1 kg water

Now we need to get rid of kg. We can look up the relationship 1kg equals 1000 grams. Put the kg part on bottom so it will cancel kg's that we have on top

 25 lb melon  0.92 lb water  1 kg water  1000 g water
   1 lb melon  2.2 lb water  1 kg water

The only units or labels not cancelled in g of water, which is exactly what the problem is asking for. When the units work out, you know that the set-up has to be correct.

Now multiply the entire numerator across. Multiply the denominator across and divide the numerator by the denominator.

 25 lb melon  0.92 lb water  1 kg water  1000 g water
   1 lb melon  2.2 lb water  1 kg water

=10,454 g of water.

Rules: 

  1. Place a single label and number in each box.
  2. Start the problem with the simplest variable given in the problem.
  3. The bottom cell of the first column is often blank. Use it only if  the variable given in the problem is a rate like miles/hr. or other compound unit.
  4. Make sure that the units really do cancel.

    

If you don't have you conversion list here one for you online: Conversions