Dimensional Analysis really hard need clear understandable help?

aroma ice cream image

Ashton

Vanillin (used to flavor vanilla ice cream and other foods) is the substance whose aroma the human nose detects inthe smallest amount. The threshold limit is 2.0x10-11g per liter of air. If the current price of 50 g of vanillin is $112,determine the cost to supply enough vanillin so that the aroma could be detected in a large aircraft hangar with a volumeof 5.0 x 107 ft3. (ans = 6.3 cents)

Answer
1 dm^3 = 0.035 ft^3.

(Numerator) (2.0 * 10^-11 g) (112 dollars) ( 1dm^3) ( 100 cents) (5 * 10^7 ft^3) /

(Denominator) (dm^3 ) (50 g) (0.035 ft^3) ( 1 dollar)

g, dm^3, dollars, ft^3 cancel out leaving cents.

Answer: 6.4 cents.