Dimensional Analysis Converting

REMEMBER THAT: ***This is a process…even if you know how to do it another way…DON’T…I am teaching you the process! A conversion factor is ALWAYS equal to one –(because when you divide something by another quantity that is equal to it, it is like dividing that number by itself, which always equals ONE)

Creating Conversion Factors STATEMENTEQUALITYCONVERSION FACTORS There are 60 seconds in a minute.1 min = 60 s1 min and 60 s 60 s 1 min There are 100 pennies in a dollar.$1 = 100¢ $1 and 100¢ 100¢ $1 There are 16 cups in a gallon. There are 1000 milliliters in a liter. There are 5280 feet in a mile. 16 cups = 1 gal 1000 mL = 1 L 5280 ft = 1 mile

NOTICE: One of the #’s in the conversion is always 1 Can apply to metric units. Bigger unit is going to be 1 STATEMENTEQUALITYCONVERSION FACTORS km to m g to cg 1g and 100cg 100cg 1g 1 km and 1000m 1000m 1 km 1 g = 100cg 1 km = 1000 m

GigaMegakilohectadecadecicentimillimicronano GMkhdadcm  n # MU # base

How to use the conversion factors. Since conversion factors have a value of 1, when you multiply by them, although the number (and units) may change, the value stays the same, since you’re just multiplying by 1.

Rules Set up a grid. (with as many sections as you need)

Rules Place # and unit of what you are given in first space of grid.

Rules Place conversion factor with unit you are given on bottom of grid and unit of what you want on top in next space.

Rules Repeat step 3 if needed.

Example 205 km = ____m 4 cg = ____g STATEMENTEQUALITYCONVERSION FACTORS km to m1 km = 1000 m1 km and 1000m 1000m 1 km g to cg 1 g = 100cg 1g and 100cg 100cg 1g = m Don’t forget units! =.04 g Don’t forget units!

Squared and Cubed Unit Conversions Sometimes it is necessary to create a conversion factor that involves a squared or cubed unit.

Barrel Cubic inches Cubic feet Cubic yards Minims Drops Gallons, imperial gallons, quarts, pints, fluid ounces, pecks, bushels

1 gram defined as the mass of one cubic centimeter of water (or one milliliter [mL] of water_.

Liter from Litron: Measure of capacity One liter of water has a mass of one kilogram

Example 1: You need a conversion factor that relates square inches (in2) and square feet (ft2). How to create the conversion factor: (square the numbers and the units!)

Complex Unit Conversions A complex unit is one that has both a numerator and a denominator. To convert complex units, just tackle the units one at a time, but in the same problem. Example 1: Convert 65 mi/hr to m/s.