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What is Dimensional Analysis?

• Dimensional Analysis (also called Factor-Label Method or the Unit Factor Method) is a problem-solving method that uses the fact that any number or expression can be multiplied by one without changing its value!

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Dimensional Analysis is not for everyone. But it's probably for

you. First of all then, who should avoid Dimensional

Analysis (DA)?

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Reasons for not using Dimensional Analysis

1. Let's say you're super-intelligent and enjoy solving relatively simple problems in the most complex manner.

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Reasons for not using Dimensional Analysis

2. Let's say you're tired of always getting the correct answers.

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Reasons for not using Dimensional Analysis

• 3. Let's say you're an arty type and you can't be confined by the structure of DA. You like messy solutions scribbled all over the page in every which direction. It's not that you want to make a mistake, but you really don't care that much about the answer. You just like the abstract design created by the free-wheeling solution... and the freedom from being confined by structure.

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Reasons for not using Dimensional Analysis

4. Let's say that you have no interest in going to the prom or making the soccer team, and you don't mind being unpopular, unattractive, ignorant, insecure, uninformed, and unpleasant.

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Otherwise,You Need Dimensional

Analysis!

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Equalities

State the same measurement in two different units

Example:

10.0 in.

25.4 cm

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Some Metric EqualitiesExamples

Length

1 m = 100 cm

Mass

1 kg = 1000 g

Volume

1 L = 1000 mL

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Some American EqualitiesExamples

1 ft = 12 inches

1 lb = 16 oz

1 quart = 2 pints

1 quart = 4 cups

The quantities in each pair give the same measured amount in two different units.

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Some Metric-American Equalities Examples

1 in. = 2.54 cm

1 qt = 946 mL

1 L = 1.06 qt

1 lb = 454 g

1 kg = 2.20 lb

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Conversion Factors

An equality expressed as a fraction

ALWAYS EQUAL TO ONE!!!!!!!!!!

Example: 1 in. = 2.54 cm

Factors: 1 in. and 2.54 cm

2.54 cm 1 in.

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Learning Check

Write conversion factors that relate each of the following pairs of units:

We Do: Liters and mL

You Do: Hours and minutes

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Solution

A. Liters and mL 1 L = 1000 mL

1 L and 1000 mL

1000 mL 1 L

B. hours and minutes 1 hr = 60 min

1 hr and 60 min

60 min 1 hr

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Steps for solving problems-

• Write the number and unit you are given.

2. Leave some space and write = and the unit you are trying to convert to.

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Steps for solving problems-3. Use conversion factors that will cancel out unwanted units until only the unit you want is left.

4. Multiply all numbers on top. Multiply all numbers on bottom. Divide last.

5. Write final answer with units.

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I Do: How many inches are in 15.5 cm?

We Do: How many liters are in 6.50 moles?

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You Do: Express 24.0 cm in inches.

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You can also string many unit factors together:

I Do: A caterpillar is 3.45 cm long. How long is the caterpillar in feet?

Unit Plan:

Solve:

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We Do: Sandra measured the length of a plant and found that it was 13.2 cm long. How long is this in yards?

Unit Plan:

Solve:

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You Do: Dave spent 30.5 minutes running around his neighborhood. How much time did he spend running in terms of years?

Unit Plan:

Solve: