Learn to use dimensional analysis to make unit conversions.
Course 2
5-4 Dimensional Insert Lesson Title Here Analysis
Vocabulary unit conversion factor
Course 2
5-4 Dimensional Analysis
cup cup cup cup
cup cup cup cup Course 2
Pint Pint
Quart
Quart
Pint Pint
Gallon
Pint Pint
Quart
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Quart Pint Pint
cup cup cup cup
5-4 Dimensional Analysis
Course 2
5-4 Dimensional Analysis
Course 2
5-4 Dimensional Analysis
Course 2
5-4 Dimensional Analysis
Course 2
5-4 Dimensional Analysis
King
km Kg
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Henry
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m L g
Drink Chocolate
cm
Mini-Milks
mm mL mg
5-4 Dimensional Analysis You can use a unit conversion factor to change, or convert, measurements from one unit to another. A unit conversion factor is a fraction in which the numerator and denominator represent the same quantity, but in different units. The fraction below is a unit conversion factor that can be used to convert miles to feet. Notice that it can be simplified to one. 5,280 ft = 5,280 ft = 1 5,280 ft 1 mi
Course 2
5-4 Dimensional Analysis Multiplying a quantity by a unit conversion factor changes only its units, not its value. The process of choosing an appropriate conversion factor is called dimensional analysis.
Course 2
5-4 Dimensional Analysis
Helpful Hint When choosing a unit conversion factor, choose the one that cancels the units you want to change and replaces them with the units you want.
Course 2
5-4 Dimensional Analysis Additional Example 1: Making Unit Conversions An oil drum holds 55 gallons. How many quarts of oil will fill the drum? Use a unit conversion factor to convert the units.
One gallon equals 4 quarts so use the conversion factor 1 gal or 4 qt . Choose the second one so the 4 qt
1 gal
gallon units will “cancel.” 55 gal · 4 qt = 55 · 4 qt 1 gal
1
Multiply.
= 220 qt 220 quarts of oil will fill the drum. Course 2
5-4 Dimensional Analysis Try This: Example 1 An ice cream recipe calls for 7 quarts of milk. How many pints of milk is this? Use a unit conversion factor to convert the units.
One quart equals 2 pints so use the conversion factor 1 qt or 2 pt . Choose the second one so the 2 pt
1 qt
quarts units will “cancel.” 2 pt = 7 · 2 pt 7 qt · 1 1 qt
Multiply.
= 14 pt 7 quarts of milk is 14 pints. Course 2
5-4 Dimensional Analysis Additional Example 2A: Making Rate Conversions Use a unit conversion factor to convert the units within each rate.
A. If orange juice sells for $1.28 per gallon, what is the cost per ounce? $1.28 · 1 gal · 1 qt = $1.28 · 1 · 1 gal 4 qt 32 oz 1 · 4 · 32 oz $1.28 = 128 oz $1.28 per gallon $1.28 ÷ 128 is $0.01 per = 128 oz ÷ 128 ounce. $0.01 = 1 oz Course 2
Multiply.
5-4 Insert LessonAnalysis Title Here Dimensional Additional Example 2B: Making Rate Conversions Use a unit conversion factor to convert the units within each rate.
B. Convert 80 miles per hour to miles per minute. 80 mi · 1 hr 80 mi · 1 = 1 hr 60 min 1 · 60 min =
80 mi ÷ 60 60 min ÷ 60
≈
1.33 mi 1 min
Multiply.
80 miles per hour is about 1.33 miles per minute. Course 2
5-4 Dimensional Analysis Try This: Example 2A Use a unit conversion factor to convert the units within each rate.
If milk sells for $2.24 per gallon, what is the cost per pint? $2.24 · 1 gal · 1 qt = $2.24 · 1 · 1 gal 4 qt 2 pt 1 · 4 · 2 pt $2.24 = 8 pt $2.24 per gallon $2.24 is $0.28 per pint. = 8 pt $0.28 = 1 pt Course 2
Multiply.
5-4 Insert LessonAnalysis Title Here Dimensional Try This: Example 2B Use a unit conversion factor to convert the units within each rate.
B. Convert 50 miles per hour to miles per minute. 50 mi · 1 hr 50 mi · 1 = 1 hr 60 min 1 · 60 min =
50 mi 60 min
≈
0.833 mi 1 min
Multiply.
50 miles per hour is about 0.83 miles per minute. Course 2
5-4 Dimensional Analysis Try This: Example 3 Mary went to the grocery store to buy 5 pounds of peaches. How many grams is this?
Use unit conversion factors that convert pounds to to kilograms, and then kilograms to grams. One kilogram is equivalent to 2.2 pounds. 5 lb ·
1 kg 2.2 lb
·
1,000 g = 5 · 1 · 1,000 g 1 kg 2.2 = 5,000 g ÷ 2.2 2.2 ÷ 2.2
2,273 g 5 pounds is about 2,273 grams. ≈
Course 2
5-4 Dimensional Insert Lesson Analysis Title Here Lesson Quiz Use a unit conversion factor to convert the units. 1. Football fields are 100 yards long. How many feet is that? 300 feet 2. In biology lab you measure a grasshopper’s wing span to be 3 inches long. How many centimeters is this? 7.62 cm Use a unit conversion factor to convert the units within a rate. 3. On a freeway a car’s speed is 62 miles per hour. What speed is that in feet per hour? 327,360 ft/h 4. If you are paid $7.50 per hour to watch your neighbor’s children, how much are you paid per minute? 12.5 cents per minute Course 2