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 FactorsSTATEMENT EQUALITY CONVERSION FACTORS

There are 60 seconds in a minute. 1 min = 60 s 1 min and 60 s60 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 1

1 16

cups galand

gal cups

5280 1

1 5280

ft mileand

mile ft

16 cups = 1 gal

1000 mL = 1 L

5280 ft = 1 mile

1000 1

1 1000

mL Land

L mL

NOTICE:

• One of the #’s in the conversion is always 1• Can apply to metric units.• Bigger unit is going to be 1

STATEMENT EQUALITY CONVERSION FACTORS

km to m

g to cg 1g and 100cg100cg 1g

1 km and 1000m1000m 1 km

1 g = 100cg

1 km = 1000 m

Giga Mega kilo hecta deca deci centi milli micro nano

G M k h da d c m n

# MU 1 1 1 1 1 101 102 103 106 109

# base

109 106 103 102 101 1 1 1 1 1

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.

#unit

Rules

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

#unit conversion unit

facto

want

git nr veuni

Rules

• Repeat step 3 if needed.

# want want

giv

unit conversion unit conversion unit

factor unit factoen gii vr en t nu

Example

• 205 km = ____m

• 4 cg = ____g

STATEMENT EQUALITY CONVERSION FACTORS

km to m 1 km = 1000 m 1 km and 1000m1000m 1 km

g to cg 1 g = 100cg 1g and 100cg100cg 1g

205 1000

1

km m

km

4 1

100

cg g

cg

= 205 000 m

Don’t forget units!

= .04 gDon’t forget units!

Squared and Cubed Unit Conversions

• Sometimes it is necessary to create a conversion factor that involves a squared or cubed unit.

BarrelCubic inchesCubic feetCubic yardsMinimsDrops

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.