Dimensional Analysis (Conversion Factors)



Dimensional Analysis (Conversion Factors)

Dimensional Analysis- a method/procedure used to convert one unit to another.

Conversion Factors- simple identities written as fractions.

We do simple conversions between different units on a daily basis. For example:

|[pic] |Question: |

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| |A statement such as this can be written as an identity. |

| |1 dozen eggs = 12 eggs |

| |Conversion Factors are identities written as fractions. Each conversion factor has two “versions.” |

| |1 dozen 12 eggs |

| |12 eggs or 1 dozen |

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| |How many eggs are there in 1 dozen eggs? _________ |

How do you set-up a dimensional analysis problem?

Example: How many eggs are there in 42 dozen?

Step 1: Identify the given value and write it down. 42 dozen

Step 2: Determine which unit you want the answer expressed in.

42 dozen x = ? eggs

Step 3: Choose your conversion factor. Your conversion factor should get you from the units you start with to the units you want to end with. The units you started with should go on the bottom of the conversion factor. The units you want to end with should go at the top of your conversion factor.

42 dozen x 12 eggs = ? eggs

1 dozen

Step 4: Do the math by multiplying across the top and dividing by the bottom.

42 dozen x 12 eggs = 504 eggs

1 dozen

Step 5: Cancel like units where possible and write the remaining unit behind your answer.

42 dozen x 12 eggs = 504 eggs

1 dozen

Task: Complete the following conversions. See your Chemistry Conversion Factor Sheet for appropriate conversion identities.

|5.51 cm to meters | |

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|23.0 ounces to pounds | |

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Question: How do you approach a problem like “Convert 55 cm into feet” – where there is no available single conversion factor?

Answer:

55 cm x ___________ x _____________ = _______________

|[pic] |Link as many conversion factors as necessary together in order to create a ‘chain’. Each ‘link’ in the |

| |chain converts one unit to another and so on until the answer is reached. |

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