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

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.

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

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

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

Section 2 Units of Measurement Chapter 2 SI Conversions

Conversion Factors, continued Section 2 Units of Measurement Chapter 2 Conversion Factors, continued Sample Problem B Express a mass of 5.712 grams in milligrams and in kilograms.

Conversion Factors, continued Section 2 Units of Measurement Chapter 2 Conversion Factors, continued Sample Problem B Solution Express 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:

Conversion Factors, continued Section 2 Units of Measurement Chapter 2 Conversion Factors, continued Sample Problem B Solution, continued Express 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:

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.