Imagine This!You’re driving along a highway in Mexico when you notice this sign

What should your speed be in miles per hour?

Dimensional Analysis

Equivalence Statements, & Conversion Factors

I) Equivalence Statements

An equivalence statement shows two quantities with different units that are equal to each other.

Equivalence Statements

A) equivalence statements can be counted numbers:

Examples: 1 dozen eggs = 12 eggs 1 pair of shoes = 2 shoes

Equivalence Statements

B) equivalence statements can be numbers with in the same measurement system:

Examples: 1 km = 1000m 5280 feet = 1 mile

Equivalence Statements

C) equivalence statements can be numbers in different measurement systems:

Examples: 1 lb = 2.21 kg 1 in = 2.540 cm

Equivalence Statements

D) equivalence statements can be numbers that are specific to a situation:

Examples:1 in = 50 km such as on a map 1m = 3.45cm such as in a photograph3 students = 1 lab group such as during a particular lab

Practice:Design four equivalence statements and write them on your paper:

II) Conversion Factors

A) Conversion factors are a set of fractions that ALWAYS equal one. The numerator and the denominator have equal value.

II) Conversion Factors

B) Every equivalence statement can be used to construct 2 conversion factors.

Practice:Write the two conversion factors for the equivalent statement below:

equivalence statements 13 steps = 1 flight of stairs

II) Conversion Factors

Use background information sheet (equivalent statements) to write base conversion factors.

III) Using Conversion Factors for Dimensional Analysis

A) What happens to the value of a number when you multiply it by one?

B) Because a conversion factor is a fraction that equals one, when it is used in a calculation it does not effect the value of the number, however, it does change the units.

III) Using Conversion Factors for Dimensional Analysis

C) Dimensional analysis is the process by which a conversion factor is used to convert a value from one unit to another.

III) Using Conversion Factors for Dimensional Analysis

D) To decide which of the two conversion factors to use make sure the units from the known value will cancel leaving units for the unknown value.

III) Using Conversion Factors for Dimensional Analysis

DO IT!!

1. Write down the given information and put it over 1.

Convert

3.5 hours to minutes:

DO IT!!

1. Get up a conversion factor such that the information in the numerator and denominator equal each other.

3.5 hrs 1

DO IT!!

1. Cancel the units 3.5 hrs X 60 min 1 1 hrs

DO IT!!

1. Multiply the numerators.

3.5 hrs X 60 min = 210 min 1 1hr

DO IT!!

1. Multiply the denominators

3.5 hrs X 60 min = 210 min 1 1hr 1

DO IT!!

1. Divide your final answer and include the new units.

3.5 hrs X 60 min = 210 min =

210min 1 1hr 1

Practice:

convert 27.5 L to mL

Convert 67.9dam to m

Convert 950g to kg