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

4 quarters 1 dollar1 1

1 dollar 4 quarters

0.25 dollar 1 quarter1 1

1 quarters 0.25 dollar

Section 2 Units of MeasurementChapter 2

Click below to watch the Visual Concept.

Visual Concept

Chapter 2 Section 2 Units of Measurement

Conversion Factor

Good, but next slide needs to further explain how to set up a conversion

problem.

Conversion Factors, continued

• Dimensional analysis is a mathematical technique that allows you to use units to solve problems involving measurements.

4 quarter? quarters 12 dollars 48 quarters

1 dollar

Section 2 Units of MeasurementChapter 2

• quantity sought = quantity given × conversion factor

• example: the number of quarters in 12 dollars

number of quarters = 12 dollars × conversion factor

Using Conversion Factors

Section 2 Units of MeasurementChapter 2

• example: conversion factors for meters and decimeters

Conversion Factors, continuedDeriving Conversion Factors

• You can derive conversion factors if you know the relationship between the unit you have and the unit you want.

1 m 0.1 m 10 dm

10 dm dm m

Section 2 Units of MeasurementChapter 2

SI Conversions

Section 2 Units of MeasurementChapter 2

Conversion Factors, continuedSample Problem B

Express a mass of 5.712 grams in milligrams and in kilograms.

Section 2 Units of MeasurementChapter 2

Conversion Factors, continuedSample Problem B SolutionExpress a mass of 5.712 grams in milligrams and in kilograms.

Given: 5.712 g

Unknown: mass in mg and kg

Solution: mg

1 g = 1000 mg

Possible conversion factors:

1000 mg 1 gand

g 1000 mg

1000 mg5 5. 7712 g m

g12 g

Section 2 Units of MeasurementChapter 2

Sample Problem B Solution, continuedExpress a mass of 5.712 grams in milligrams and in kilograms.

Given: 5.712 g

Unknown: mass in mg and kg

Solution: kg

1 000 g = 1 kg

Possible conversion factors:

Conversion Factors, continued

1000 g 1 kgand

kg 1000 g

1 kg5.712 g

10000.005

g712 kg

Section 2 Units of MeasurementChapter 2

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

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.

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

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

1 0.62 mi 0.62

Notice that the miles cancel out, and your new unit is km.

96.8 km/h is the same as 60 mi/h.