(Dimensional Analysis)

A. Create CONVERSION FACTORS You can divide both sides of an equation by the same number and it does not change the value of the equality. So if we take the equality 100 cm= 1m, we can divide both sides by 1 m. 100cm = 1m 1m 1m Both sides of this equation are equal to 1.

You can multiply any number by 1 and it does not change the numerical value. That means I can multiply anything I want by 100cm 1m because it is equal to the number 1. Alternatively, I can multiply anything I want by the inverse relationship, 1m_ 100cm which is also equal to 1.

Write conversion factors to represent the following equalities: a)1 m 3 = cm 3 b)1 in = 2.54 cm c)1 g = 1000 mg d)1 000 m = 1 km

a)1m cm cm 3 1m 3 b)1in_2.54 cm 2.54cm 1 in c) 1 g____ 1000 mg 1000 mg 1 g d) 1 000m____ 1 km 1 km 1 000m

B. Which conversion factor?  There are numerous conversion factors that can be created.  Anytime you are given an equality (something with an equal sign) you can create a conversion factor  You need to use your brain to figure out which conversion factor you need and how to use it…put your brain to work!!

C. Solving problems: 1. Look at the units given in the problem. 2. Look at what is being asked in the problem (answer should be in what units?). 3. Look for unit conversion factors to get from what is given to what is asked for.

4. For each step, create a conversion factor so a numerator from one step cancels a denominator from another step: denominator: what units you start with numerator: what units you want to end with 5. Use a solution map to visualize the route required to solve the problem Starting Units > Steps > Ending Units

Ex: How many meters are in 12 kilometers? 1. Given: 12 km 2. solve for: meters (m) 3. create conversion factor….so think: denominator to be “km” numerator to be “m” 1000m___ 1 km

Solve: 12 km x 1000 m = 12000m 1km (think multiplication with S.F.)

Ex: Given 1 in = 2.54 cm How many inches are found in 102 cm? 1. Given: 102 cm 2. solve for: inches 3. create conversion factor….so think: denominator to be “cm” numerator to be “in” 1in___ 2.54cm 4. Visualize if you need more than one conversion factor

Solve: 102 cm x 1 in = 40.2 in 2.54cm (think division with S.F. for rounding!!)

Ex: Given 1 liter = 1.06 quarts, How many liters are in 2.63 qt? 2.63 qt x 1 liter = 2.48 liter 1.06qt Answer: 2.48 liters

With metric conversions, it is often easiest to convert each prefix with its base and then to the prefix you wish to have. Ex. How many cm are found in 15.5 km? Go from: km m cm 15.5 km x 1000m x 100 cm = 15,500,000cm 1 km 1m