1. 5-4 Dimensional Analysis Course 2 Warm Up Warm Up Problem of the Day Problem of the Day Lesson Presentation Lesson Presentation

2. Warm Up Use cross products to solve the proportions. Course 2 5-4 Dimensional Analysis 1. 2. 3. 4. n = 25 r = 24 k = 36 x = 12 40 x = 30 9 3838 = r 64 9 17 = k 68 6 10 = 15 n

3. Problem of the Day The sum of four consecutive integers is 182. What are the four numbers? 44, 45, 46, and 47 Course 2 5-4 Dimensional Analysis

4. Learn to use dimensional analysis to make unit conversions. Course 2 5-4 Dimensional Analysis

5. Vocabulary unit conversion factor Insert Lesson Title Here Course 2 5-4 Dimensional Analysis

6. Course 2 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 1 mi = 5,280 ft = 1

7. 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.

8. Course 2 5-4 Dimensional Analysis 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. Helpful Hint

9. An oil drum holds 55 gallons. How many quarts of oil will fill the drum? Use a unit conversion factor to convert the units. Additional Example 1: Making Unit Conversions Course 2 5-4 Dimensional Analysis 55 gal · = 220 qt 220 quarts of oil will fill the drum. Multiply. One gallon equals 4 quarts so use the conversion factor or. Choose the second one so the 1 gal 4 qt 1 gal gallon units will “cancel.” = 4 qt 1 gal 55 · 4 qt 1

10. Try This: Example 1 Course 2 5-4 Dimensional Analysis 7 qt · = 14 pt Multiply. One quart equals 2 pints so use the conversion factor or. Choose the second one so the 1 qt 2 pt 1 qt quarts units will “cancel.” = 2 pt 1 qt 7 · 2 pt 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. 7 quarts of milk is 14 pints.

11. Use a unit conversion factor to convert the units within each rate. Additional Example 2A: Making Rate Conversions Course 2 5-4 Dimensional Analysis A. If orange juice sells for $1.28 per gallon, what is the cost per ounce? $1.28 gal · 1 gal 4 qt · 1 qt 32 oz = $1.28 · 1 · 1 1 · 4 · 32 oz Multiply. = $1.28 128 oz = $1.28 ÷ 128 128 oz ÷ 128 = $0.01 1 oz $1.28 per gallon is $0.01 per ounce.

12. Insert Lesson Title Here 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 · 60 min Multiply. = 80 mi ÷ 60 60 min ÷ 60 ≈ 1.33 mi 1 min 80 miles per hour is about 1.33 miles per minute. Additional Example 2B: Making Rate Conversions Course 2 5-4 Dimensional Analysis 1 hr 60 min =

13. Use a unit conversion factor to convert the units within each rate. Course 2 5-4 Dimensional Analysis $2.24 gal · 1 gal 4 qt · 1 qt 2 pt = $2.24 · 1 · 1 1 · 4 · 2 pt Multiply. = $2.24 8 pt = $2.24 8 pt = $0.28 1 pt $2.24 per gallon is $0.28 per pint. Try This: Example 2A If milk sells for $2.24 per gallon, what is the cost per pint?

14. Insert Lesson Title Here 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 · 60 min Multiply. = 50 mi 60 min ≈ 0.833 mi 1 min 50 miles per hour is about 0.83 miles per minute. Try This: Example 2B Course 2 5-4 Dimensional Analysis 1 hr 60 min =

15. The Mare Orientale crater on the Moon is more than 620 miles across. How many meters is this? Additional Example 3: Measurement Application Course 2 5-4 Dimensional Analysis Use unit conversion factors that convert miles to to kilometers, and then kilometers to meters. One kilometer is equivalent to 0.62 mile. 620 mi · 620 · 1 · 1,000 m 0.62 = 620,000 m ÷ 0.62 0.62 ÷ 0.62 = 1,000,000 m 620 miles is 1,000,000 meters. · 1 km 0.62 mi 1,000 m 1 km =

16. Course 2 5-4 Dimensional Analysis 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 · 5 · 1 · 1,000 g 2.2 = 5,000 g ÷ 2.2 2.2 ÷ 2.2 ≈ 2,273 g 5 pounds is about 2,273 grams. · 1 kg 2.2 lb 1,000 g 1 kg = Try This: Example 3 Mary went to the grocery store to buy 5 pounds of peaches. How many grams is this?

17. Lesson Quiz Insert Lesson Title Here Course 2 5-4 Dimensional Analysis Use a unit conversion factor to convert the units. 1. Football fields are 100 yards long. How many feet is that? 2. In biology lab you measure a grasshopper’s wing span to be 3 inches long. How many centimeters is this? 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? 4. If you are paid $7.50 per hour to watch your neighbor’s children, how much are you paid per minute? 300 feet 7.62 cm 327,360 ft/h 12.5 cents per minute