SEVENTH EDITION and EXPANDED SEVENTH EDITION

Transcription

1 SEVENTH EDITION and EXPANDED SEVENTH EDITION Slide 8-1

2 Chapter 8 The Metric System

3 8.1 Basic Terms and Conversions within the Metric System

4 SI System and U.S. Customary System Most countries of the world use the SI system The SI system is referred to as the metric system in the United States. Two systems of weights and measures exist side by side in the United States today, U.S customary system and the metric system. Slide 8-4

5 Advantages to Using the Metric System The metric system is the worldwide accepted standard measurement system. There is only one unit of measurement for each physical quantity. The SI system is based on the number 10, allowing less need for fractions. Slide 8-5

6 Basic Terms Metric Term Abbrev. Common Use Comparison to Customary meter m length a little more than a yard. kilogram kg mass about 2.2 pounds liter L volume a little more than a quart Slide 8-6

7 Metric Prefixes Prefix kilo hecto deka deci centi milli Symbol k h da d c m 1000 base unit 100 base unit 10 base unit Meaning base unit of base unit of base unit of base unit Slide 8-7

8 Changing Units within the Metric System To change from a smaller unit to a larger unit move the decimal point in the original quantity one place to the left for each larger unit of measure until you obtain the desired unit of measure. To change from a larger unit to a smaller unit, move the decimal point in the original quantity one place to the right for each smaller unit of measurement until you obtain the desired unit of measure. Slide 8-8

9 Example: Changing Units Convert 54.6 m to km. Convert 15 L to ml. Convert 0.89 kg to cg. Solutions: Meters is a smaller unit than km. Move the decimal 3 places to the left, Liter is a larger unit than milliliter. Move the decimal point 3 places to the right, 15, kg = 89,000 cg Slide 8-9

10 Example: Application A case of fruit juice contains twenty-four 0.75 liter bottles. How many 250 milliliter glasses can you fill using one case of juice? Solution: The case of juice contains 24(0.75) = 18 L. Converting 18 L = 18,000 ml. If each glass hold 250 ml, then 18,000 glasses can be filled. 250 = 72 Slide 8-10

11 8.2 Length, Area, and Volume

12 Length The meter is used to measure things that we normally measure in yards and feet. Centimeters and millimeters are used to measure what we normally measure in inches. A centimeter is a little less than a half of an inch. A millimeter is about the thickness of a dime. Example: The length of a pair of scissors would be measured in centimeters. Slide 8-12

13 Area Areas are always expressed in square units. Example: The length of a rectangular park is 82.5 m, and its width is 25.4 m. Find the area of the park. Solution: Area = length width. A A = = m 2 Slide 8-13

14 Volume When a figure has three dimensions; length, width and height, the volume can be found. The volume of an item can be considered the space occupied by the item. Volume can be expressed in terms of liters or cubic meters. Volume in Cubic Units Volume in Liters 1 cm 3 = 1 ml 1 dm 3 = 1 L 1 m 3 = 1 kl Slide 8-14

15 Volume When the volume of a liquid is measured, the abbreviation cc is often used instead of cm 3 to represent cubic centimeters. Example: An asthma patient must mix 0.25 cc of a bronchodilator with 2 cc of saline to use in an aerosol machine. How many milliliters of the bronchodilator will be administered? What is the total volume of drug and saline solution in milliliters? Slide 8-15

16 Volume continued Solution: Since 1 cc is equal in volume to 1 milliliter, there will be 0.25 milliliters of the bronchodilator. The total volume is or 2.25 cc, which is equal to 2.25 ml. Slide 8-16

17 Example: Volume Application A cylindrical shampoo bottle has a diameter of 6 cm and a height of 12 cm. What is the volume in milliliters? Solution: 2 V = πr h V V V = = = ( ) cm ml 3 Slide 8-17

18 8.3 Mass and Temperature

19 Mass Although weight and mass are not the same, on Earth they are proportional to each other. Mass is a measure of the amount of matter in an object. Weight is the measure of gravitational pull on an object. Slide 8-19

20 Metric System The kilogram is the basic unit of mass in the metric system. Example: A man has the mass of about 75 kg. The gram is relatively small and used in place of the ounce. Example: A nickel has the mass of about 5 g. The milligram is used in the medical and scientific fields. The metric tonne is used to express mass of heavy items. One metric tonne = 1000 kg. Slide 8-20

21 Example: Choosing an Appropriate Unit Determine which metric unit you would use to express the mass of the following. a) A spider c) A bicycle b) A nickel d) A nickel Solution: a) Milligrams c) Kilograms b) Grams d) Grams Slide 8-21

22 Volume and Mass of Water Volume in Cubic Units Volume in Liters 1 cm 3 = 1 ml = 1 g 1 dm 3 = 1 L = 1 kg Mass of Water 1 m 3 = 1 kl = 1 t (1000 kg) Slide 8-22

23 Example: Capacity A fish tank is 1 m long, 60 cm high and 260 mm wide. Determine the number of liters that the tank holds. What is the mass of the water in kilograms. Slide 8-23

24 Example: Capacity continued Solution: V = l w h = = m 3 Since 1 m 3 of water = 1 kl of water, m 3 = kl, or 156 liters of water Since 1L = 1 kg, 156 L = 156 kg of water. Slide 8-24

25 Temperature ( ) The term degrees Celsius o C is used to measure temperature. o C 0 o 22 C o C Temperature o F o F o F Description Water freezes Comfortable room o C o C o F o F Body temperature Water boils Slide 8-25

26 Example: Choose o F or o C. The temperature of a can of frozen juice about 2. The temperature of a person with a fever is about The temperature of a bowl of hot soup is about 175. Solution: a) o o C. b) F c) o F Slide 8-26

27 Conversions To covert from Celsius to Fahrenheit use the following formula. To covert from Fahrenheit to Celsius use the following formula. 9 F C 32 5 = + C= ( F 32) 5 9 Slide 8-27

28 Example: Conversions The air temperature on a warm summer day is o about 85 F. What is the equivalent temperature on the Celsius thermometer? Solution: 5 C= ( F 32) 9 5 C= C= ( 53) 9 C 29.4 ( ) The equivalent temperature is o about 29.4 C. Slide 8-28

29 Example: Conversions The temperature of a cold glass of milk is o about 5 C. What is the equivalent temperature on the Fahrenheit thermometer? Solution: 9 F= C F= ( 5) F= F= 41 The equivalent temperature is about o 41 F. Slide 8-29

30 8.4 Dimensional Analysis and Conversions to and from the Metric System

31 Dimensional Analysis Dimensional analysis is a procedure used to convert from one unit of measurement to a different unit of measurement. A unit fraction is any fraction in which the numerator and denominator contain different units and the value of the fraction is 1. Examples of unit fractions: 16 oz 1 hr 12 in. 1 lb 60 min 1 ft Slide 8-31

32 U.S. Customary Units U.S. Customary Units 1 foot = 12 inches 1 quart = 2 pints 1 yard = 3 feet 1 gallon = 4 quarts 1 mile = 5280 feet 1 minute = 60 seconds 1 pound = 16 ounces 1 hour = 60 minutes 1 ton = 2000 pounds 1 day = 24 hours 1 cup (liquid) = 8 fluid ounces 1 year = 365 days 1 pint = 2 cups Slide 8-32

33 Example: Using Dimensional Analysis A recipe calls for 8 cups of blueberries. How many pints is this? Solution: 1 pint 8 cups = ( 8 cups) = 4 pint s 2 cups Convert 75 miles per hour to inches per minute. Solution: ( 75)( 5280)( 12) mi mi 5280ft 12 in 1 hr in 75 = 75 hr hr 1 mi 1 ft 60 min = 60 min in = 79,200 min Slide 8-33

34 Conversion to and from the Metric System Slide 8-34

35 Example: Volume and Area A gas tank holds 22.6 gallons of gas. How many liters is this? 3.8 L Solution: 22.6 gal = = L gal The area of a box is in 2. What is its area in square centimeters? Solution: 6.5 cm in = cm 1 in Slide 8-35

36 Example: Converting Speed A road in Toronto, Canada shows that the speed limit is 62 kph. Determine the speed in miles per hour. Solution: 1 mi km = mi = mi 1.6 km 1.6 Since 62 km equals mi, 62 kpm is equivalent to mph. Slide 8-36

37 Example: Weight (Mass) Conversion for Medication A newborn baby weighs 8 pounds 4 ounces. If 20 mg of a medication is given for each kilogram of the babies weight, what dosage should be given?. Solution: 16 oz 8 lbs 128 oz 4 oz 132 oz 1 lb = + = 28 g 1 kg 20 mg 132 oz kg mg oz = = 1000 g 1 kg The dosage of the medication is mg. Slide 8-37