Dimensional analysis ii
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Dimensional Analysis II. Beyond Simple Conversion Problems: Identifying the GIVEN and the DESIRED in Word Problems. Basic Steps in Dimensional Analysis. Identify the GIVEN value/quantity. Identify the DESIRED value/quantity. Identify the CONVERSION FACTOR(S).

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Dimensional Analysis II

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Dimensional analysis ii

Dimensional Analysis II

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


Basic steps in dimensional analysis

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.


Identification clues

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.”


Setting up the problem

Setting Up the Problem

Convert 2.000 gallons to milliliters.

7569 mL


Dimensional analysis ii

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


Dimensional analysis ii

Given Conversion Factors Desired

8.1 ÷ 2.47 ÷ 0.125 = 26 sheep


Dimensional analysis ii

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


Dimensional analysis ii

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)


Dimensional analysis ii

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

54 grams

How many ounces?

16 ounces per 454 g


Dimensional analysis ii

Given Conversion(s)Desired

54 x 16 ÷ 454 = 1.90 ounces


Dimensional analysis ii

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.


Dimensional analysis ii

Given Conversion(s) Desired

50 x 5280 ÷ 60 ÷ 60 = 73.3 Ft per Sec


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