1. Chapter 2 Conversion Factors
Section 2 Units of Measurement
Chapter 2
Conversion Factors
A conversion factor is a ratio derived from the equality between two different units that can be used to convert from one unit to the other.
example: How quarters and dollars are related

2. Chapter 2 Conversion Factor Section 2 Units of Measurement
Click below to watch the Visual Concept.
Visual Concept
 Good, but next slide needs to further explain how to set up a conversion problem.

3. Conversion Factors, continued
Section 2 Units of Measurement
Chapter 2
Conversion Factors, continued
Dimensional analysis is a mathematical technique that allows you to use units to solve problems involving measurements.
quantity sought = quantity given × conversion factor
example: the number of quarters in 12 dollars
number of quarters = 12 dollars × conversion factor

4. Using Conversion Factors
Section 2 Units of Measurement
Chapter 2
Using Conversion Factors

5. Conversion Factors, continued
Section 2 Units of Measurement
Chapter 2
Conversion Factors, continued
Deriving Conversion Factors
You can derive conversion factors if you know the relationship between the unit you have and the unit you want.
example: conversion factors for meters and decimeters

6. Section 2 Units of Measurement
Chapter 2
SI Conversions

7. Conversion Factors, continued
Section 2 Units of Measurement
Chapter 2
Conversion Factors, continued
Sample Problem B
Express a mass of grams in milligrams and in kilograms.

8. Conversion Factors, continued
Section 2 Units of Measurement
Chapter 2
Conversion Factors, continued
Sample Problem B Solution
Express a mass of grams in milligrams and in kilograms.
Given: g
Unknown: mass in mg and kg
Solution: mg
1 g = 1000 mg
Possible conversion factors:

9. Conversion Factors, continued
Section 2 Units of Measurement
Chapter 2
Conversion Factors, continued
Sample Problem B Solution, continued
Express a mass of grams in milligrams and in kilograms.
Given: g
Unknown: mass in mg and kg
Solution: kg
1 000 g = 1 kg
Possible conversion factors:

10. More about Dimensional Analysis
While most find it easier to convert metric units by moving the decimal place rather than by using a conversion factor, some conversions lend themselves better to dimensional analysis. For example: 7 yds = _____ ft To solve, we must have a conversion factor for yards and feet. 3 feet = 1 yd, so the conversion factors are either: __1 yd__ or ___3 ft___ 3 ft 1 yd

11. More about Dimensional Analysis
For example: 7 yds = _____ ft We start by writing our given amount over 1. Then we choose the appropriate conversion factor which will allow the units to cancel out (that means the given unit has to be on top of one fraction and on the bottom of the other fraction). __7 yd__ x ___3 ft___ = __21 ft__ = 21 ft 1 1 yd 1 ***Notice that the yards unit which appeared on both the top and bottom of the fraction bar cancel out, leaving only feet in your answer.

12. More on dimensional analysis
Suppose you want to change mi/h to km/h, as in our introductory problem. 60 miles per hour = _____ kilometers per hour First we must know that one kilometer = 0.62 miles. Then we write a conversion factor: __0.62 mi__ or __1 km__ 1 km 0.62 mi

13. More on dimensional analysis
60 miles per hour = _____ kilometers per hour First we write our given measurement over 1. Then multiply by the appropriate conversion factor. __60 mi__ x __1 km__ = __60_km_ = 96.8 km mi 0.62 Notice that the miles cancel out, and your new unit is km km/h is the same as 60 mi/h.