1. Dimensional Analysis II Beyond Simple Conversion Problems: Identifying the GIVEN and the DESIRED in Word Problems

2. Basic Steps in Dimensional Analysis Identify the GIVEN value/quantity. Identify the DESIRED value/quantity. Identify the CONVERSION FACTOR(S). Set up the problem with the GIVEN first and the DESIRED last-- this will just be a blank space with an attached unit or units. Put in “bridging” conversion factors which will cancel units UP/DOWN such that the DESIRED unit(s) will come through un- cancelled. Do the math: multiply factors together that are in the numerators and divide by factors that are in the denominators.

3. Identification Clues The GIVEN is usually a number all by itself with no implied equality with something else. The DESIRED has a question word associated with it: How many, How much, What is the total cost, etc. CONVERSION FACTORS are (1) a pair of numbers with explicit or implicit equality or (2) an explicit “something per something.”

4. Setting Up the Problem GIVENCONV. DESIRED FACTOR 2.000 GALS. 4 QTS.1 LITER 1000 mL 1 GAL. 1.057 QTS. LITER 7569 mL Convert 2.000 gallons to milliliters.

5. Ruth wanted to raise sheep on 8.1 acres of property. If it takes 0.125 hectare to raise one sheep, how many sheep can be raised on the property. There is one hectare per 2.47 acres. Given: Desired: Conversion(s) 8.1 acres How many sheep? 0.125 hectare per sheep 1.0 hectare per 2.47 acres

6. Given Conversion Factors Desired 8.1 ÷ 2.47 ÷ 0.125 = 26 sheep 8.1 acreshectare1 sheep= sheep 2.47 acres 0.125 hectare

7. A fast food worker wraps 350 hamburgers every hour. He works 8 hours per day. He works 5 days a week. He gets paid every 2 weeks with a salary of $440.34 (after taxes). How many hamburgers will he have to wrap to make his first one million dollars? Given: Desired: Conversion(s) $1,000,000 How many hamburgers? $440.34 per 2 weeks 5 days per week 8 hours per day 350 burgers per hour

8. Given Conversion(s) Desired 1,000,000 x 2 x 5 x 8 x 350 ÷ 440.34 = 63.6 million hamburgers wrapped (63,600,000) $1,000,000 2 wks.5 days8 hours 350 HB= HB $440.34 wkdayhour

9. How many ounces in 54 grams? (There are 16 ounces per 454 g). 16 ounces 454 g Given: Desired: Conversion(s) 54 grams How many ounces? 16 ounces per 454 g

10. Given Conversion(s) Desired 54 Grams16 ounces= ounces 454 grams 54 x 16 ÷ 454 = 1.90 ounces

11. If you are going 50 miles per hour, how many feet per second are you traveling? (5280 feet per mile). In this problem, the GIVEN looks the same as a CONVERSION FACTOR. It makes it harder to identify!! 5280 Feet Mile Given: Desired: Conversion(s) 50 miles per hour How many feet per sec? 5280 feet per mile, and you should know the ones for time.

12. Given Conversion(s) Desired 50 x 5280 ÷ 60 ÷ 60 = 73.3 Ft per Sec 50 Miles 5280 Ft.HourMin= Feet HourMile60 Min60 SecSec