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Dimensional Analysis In Chemistry (and other scientific disciplines) it is often necessary to convert measurements from one unit to another. This practice is known as dimensional analysis and utilizes what are known as conversion factors. All data (numbers) in Chemistry must be accompanied by units! Students often balk at using dimensional analysis; but since throughout the course, you will be using unfamiliar units and changing those units, make the most of this technique. Dimensional analysis will help you solve virtually problem you encounter. If you can justify the units, then you know that you have successfully converted the units and can complete the problem.

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Conversion Factors A conversion factor is a ratio in which the numerator and denominator are equivalent. Example: 12 inches = 1 foot Therefore ~ 12 inches OR 1 foot 1 foot 12 inches While the resulting numbers are different, 12 versus 1/12 (0.0833), we know that the values are equivalent.

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Using conversions factors Let’s say you are 6 feet tall. Then how many inches tall are you? What do you think? Did you say 72 inches tall? What did you do? Multiply by 12? If that’s the case let’s look at what’s right (or wrong) about your process.

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6 feet x 12 = 72 feet That’s not what you meant! How can we “fix it? Check it out using dimensional analysis 6 feet x 12 inches = 72 inches 1 foot Why? 6 feet x 12 inches = 72 inches 1 foot Notice the person’s height hasn’t actually changed, you have simply converted to a new set of units. All you have done is cancel out the appropriate units!

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Note that dimensional analysis can be used for conversion of a single unit or a series of units. Example Problem~ A snail crawls at a speed of 12 cm/min. How fast does a snail crawl in km/ hr? Note that the snail’s speed isn’t going to change; you are simply expressing it in different units. 12 cm x 1 m x 1 km x 60 min = 0.0072 km min 100cm 1000 m 1 hr hr NOTE: Only multiplication and division are required.

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1. Ratio: A comparison of 2 numbers by division. i.e.a to b a:ba/b 2. Rate: When a ratio is made up of DIFFERENT units. i.e.3in/4ft$2/5 days UNIT RATE:

1. Ratio: A comparison of 2 numbers by division. i.e.a to b a:ba/b 2. Rate: When a ratio is made up of DIFFERENT units. i.e.3in/4ft$2/5 days UNIT RATE:

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