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Dimensional Analysis II

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Dimensional Analysis II

Beyond Simple Conversion Problems: Identifying the GIVEN andthe DESIREDin Word Problems

- 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.

- 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.”

Convert 2.000 gallons to milliliters.

7569 mL

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.

8.1 acres

How many sheep?

0.125 hectare per sheep

1.0 hectare per 2.47 acres

Given Conversion Factors Desired

8.1 ÷ 2.47 ÷ 0.125 = 26 sheep

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?

$1,000,000

How many hamburgers?

$440.34 per 2 weeks

5 days per week

8 hours per day

350 burgers per hour

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)

How many ounces in 54 grams? (There are 16 ounces per 454 g).

54 grams

How many ounces?

16 ounces per 454 g

Given Conversion(s)Desired

54 x 16 ÷ 454 = 1.90 ounces

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!!

50 miles per hour

How many feet per sec?

5280 feet per mile, and you should know the ones for time.

Given Conversion(s) Desired

50 x 5280 ÷ 60 ÷ 60 = 73.3 Ft per Sec