Dimensional Analysis

Measurement Ratios In order to use dimensional analysis, you have to understand that you need to use ratios that have a value of 1 to change the units of measurement. Example 60 sec 5280 ft 12 in 1 min1 mile1 ft These are all examples of ratios that equal 1 because the measurement in the numerator is equal to the measurement in the denominator.

Cross Reducing Just as you cross reduce fractions whenever possible, you want to cross reduce the units of measurement until you get the units you want in your answer. Example: ½ x ⅔ You cross reduce the 2s to get the answer ⅓ 25 mi x 2 hr 1 hr 120 min The hr unit of measurement cancels out so that all that is left is miles/minutes.

Example Problem A car is traveling 65 miles/hr. How many feet per second is it traveling? 65 miles x 5280 ft. x 1 hour x 1 minute = feet 1 hour 1 mile 60 min 60 sec sec Cancel out all units of measurement that can be cross reduced. When all that is left is feet/sec, which is what you want, then you just work with the numbers. 65 x 5280 x 1 x Now cross reduce as much as you can, multiply across, then divide. The result will be the number of feet per second you are traveling when going 65 mph. Answer: 95.3 feet/sec

Practice Problems How many seconds are there in one week? How many ounces are in one ton? How many cups in one gallon?