Chapter 1 Dimensional Analysis (or, Converting Units)

Chapter 1Chapter 1

Dimensional AnalysisDimensional Analysis(or, Converting Units)(or, Converting Units)

Something you probably know how to Something you probably know how to do….do….

How many seconds are in one day?

Math ReviewMath Review

2

2

41

41

918

918

All equal 1!You can think of units like numbers…

1meters

meters

Converting UnitsConverting Units

Conversion Factor: Conversion Factor: two measurements that are two measurements that are equal, but equal, but have different unitshave different units Examples: Examples:

• 1 foot = 12 inches1 foot = 12 inches• 100 cm = 1 meter100 cm = 1 meter• 60 seconds = 1 minute60 seconds = 1 minute

Dimensional Analysis: Dimensional Analysis: a fancy name for a fancy name for “converting units” “converting units”

Conversion FactorsConversion Factors

What is the value of the following:What is the value of the following:

1 minute 1

seconds 60

Conversion factors can be flipped as needed Conversion factors can be flipped as needed because the ratio equals 1because the ratio equals 1::

seconds 60

minute 1or

minute 1

seconds 60

?

Steps to Converting UnitsSteps to Converting Units

Step 1:Step 1: Write down the given quantity and unit. Write down the given quantity and unit.

EXAMPLE: EXAMPLE: Convert 18000 seconds to hours.Convert 18000 seconds to hours.

Step 2: Step 2: List all necessary conversion factors. List all necessary conversion factors. ( # with unit = # with unit)( # with unit = # with unit)

Step 3:Step 3: Begin writing the conversion factors as Begin writing the conversion factors as fractions multiplied together.fractions multiplied together.

Converting UnitsConverting UnitsEXAMPLE:EXAMPLE:

The ninth grade class at Irondale is having a pizza reward lunch for collecting the most The ninth grade class at Irondale is having a pizza reward lunch for collecting the most food in a food drive. Each student will get 2 slices of pizza. Each pizza has 12 slices. There food in a food drive. Each student will get 2 slices of pizza. Each pizza has 12 slices. There are 450 students total in ninth grade. How many pizzas need to be ordered?are 450 students total in ninth grade. How many pizzas need to be ordered?