Conversions by Dimensional Analysis & Moving the Decimal

Please do this now. Fewest equations wins a prize. I made apple pies this weekend for a party. Each pie called for 2 cups of sliced apples. It took 1.5 apples to make 1 cup of sliced apples. Each pie I made served 6 people. How many apples were in each serving of my apple pie?

Let’s use Dimensional Analysis

First things first – identify conversion factors. 2 cups sliced apples = 1 pie 1.5 apples = 1 cup of sliced apples 1 pie = 6 servings 2 cups of sliced apples= 1 =1 pie 2 cups of sliced apples 1.5 apples= 1 =1 cup of sliced apples 1.5 apples 1 pie= 1 =6 servings 1 pie

Now – what units do you want to end up with? How many apples were in each serving of my pie? =apples serving

Then – set up an equation to get to final, desired units, using your conversion factors. =apples serving 1.5 apples2 cups of sliced apples1 pie 1 cup of sliced apples 1 pie6 servings 2 cups of sliced apples= 1 =1 pie 2 cups of sliced apples 1.5 apples= 1 =1 cup of sliced apples 1.5 apples 1 pie= 1 =6 servings 1 pie

Finally, do the math and solve the equation. =0.5 apples serving 1.5 x 2x 1 (apples)3 apples 1x1x6 (servings)6 servings

Try the same method with metric conversions. 1 kg = 1000 g = 1 x 10 3 g 1 hg = 100 g = 1 x 10 2 g 1 dag = 10 g = 1 x 10 1 g 1 g = 1 g = 1 x 10 0 g 1 dg = 0.1 g = 1 x g 1 cg = 0.01 g = 1 x g 1 mg = g = 1 x g (kids) (have) (d’ropped) (over) (dead) (converting) (metrics) 1 Gg = 1 x 10 9 g 1 Mg = 1 x ug = 1 x g 1 ng = 1 x g 1 pg = 1 x g