1. Copyright © 2009 Pearson Education, Inc. Welcome to MM150! Unit 5 Seminar To resize your pods: Place your mouse here. Left mouse click and hold. Drag to the right to enlarge the pod. To maximize chat, minimize roster by clicking here

2. Copyright © 2009 Pearson Education, Inc. MM150 Unit 5 Seminar Agenda Metric System Length, Area, and Volume Mass and Temperature Conversion to and from the Metric System

3. Copyright © 2009 Pearson Education, Inc. 5.1 Basic Terms and Conversions within the Metric System

4. Copyright © 2009 Pearson Education, Inc. SI System and U.S. Customary System U.S customary system Systéme international d’unités or SI system. referred to as the metric system

5. Copyright © 2009 Pearson Education, Inc. Advantages to Using the Metric System Accepted worldwide standard measurement Only one unit of measurement Based on the number 10 Less need for fractions

6. Copyright © 2009 Pearson Education, Inc. Basic Terms a little more than a quart volumeLliter about 2.2 pounds masskgkilogram a little more than a yard lengthmmeter Comparison to Customary Common Use AbbrevMetric Term

7. Copyright © 2009 Pearson Education, Inc. Metric Prefixes 1/1000 of base unitmmilli 1/100 of base unitccenti 1/10 of base unitddeci base unit 10  base unit dadeka 100  base unit hhecto 1000  base unit kkilo MeaningSymbolPrefix

8. Copyright © 2009 Pearson Education, Inc. Changing Units within the Metric System Measure of length kilometerhectometerdekameter Symbolkmhmdam Number of meters 1000 m100 m10 m Measure of length meterdecimetercentimetermillimeter Symbolmdmcmmm Number of meters 1 m0.1 m0.01 m0.001 m

9. Copyright © 2009 Pearson Education, Inc. Example: Changing Units Convert 54.6 m to km. Solution: Meters is a smaller unit than km. There are 1000 m in one km. Divide 54.6m/1000 or … Move the decimal 3 places to the left, 0.0546 km.

10. Copyright © 2009 Pearson Education, Inc. Example: Changing Units Convert 15 L to mL. Hint. There are 1000 mL in one Liter.

11. Copyright © 2009 Pearson Education, Inc. Example: Changing Units Convert 15 L to mL. Solution: Liter is a larger unit than milliliter. There are 1000 mL in one L. Multiply 15L * 1000 or … Move the decimal point 3 places to the right, 15,000 mL.

12. Copyright © 2009 Pearson Education, Inc. Example: Changing Units Convert 0.89 kg to cg. Hint. There are 100 centigrams in one gram, and 1000 grams in one kilogram.

13. Copyright © 2009 Pearson Education, Inc. Example: Changing Units Convert 0.89 kg to cg. Solutions: Kilogram is a larger unit than centigram. There are 100 centigrams in one gram, and 1000 grams in one kilogram. Multiply 0.89 kg * 100,000 or … Move the decimal point 5 places to the right 0.89 kg = 89,000 cg

14. Copyright © 2009 Pearson Education, Inc. 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 glasses can be filled.

15. Copyright © 2009 Pearson Education, Inc. 5.2 Length, Area, and Volume

16. Copyright © 2009 Pearson Education, Inc. 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.

17. Copyright © 2009 Pearson Education, Inc. Area Areas are always expressed in square units. Example: The length of a rectangular park is 8m, and its width is 2m. Find the area of the park. Solution: Area = length  width. A = 8m x 2m A = 16m 2

18. Copyright © 2009 Pearson Education, Inc. Volume When a figure has three dimensions; length, width and height, the volume can be found. The volume of an item is how much can be held by the item. Volume can be expressed in terms of liters or cubic meters. 1 m 3 = 1 kL 1 dm 3 = 1 L 1 cm 3 = 1 mL Volume in LitersVolume in Cubic Units

19. Copyright © 2009 Pearson Education, Inc. 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?

20. Copyright © 2009 Pearson Education, Inc. Volume continued Example: An asthma patient must mix 0.25 cc of a bronchodilator with 2 cc of saline to use in an aerosol machine. Solution: Since 1 cc is equal in volume to 1 milliliter, there will be 0.25 milliliters of the bronchodilator. The total volume is 0.25 + 2 or 2.25 cc, which is equal to 2.25 mL.

21. Copyright © 2009 Pearson Education, Inc. 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:V = (Area base)h V = πr 2 h V = 3.14(3) 2 12 V = 339.12 cm 3 V = 339.12 mL 6cm

22. Copyright © 2009 Pearson Education, Inc. 5.3 Mass and Temperature

23. Copyright © 2009 Pearson Education, Inc. 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.

24. Copyright © 2009 Pearson Education, Inc. 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 (t) is used to express mass of heavy items. One metric tonne = 1000 kg.

25. Copyright © 2009 Pearson Education, Inc. 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 box of cereal Solution: a) Milligrams c) Kilograms b) Grams d) Grams

26. Copyright © 2009 Pearson Education, Inc. Volume and Mass of Water Volume in Cubic Units 1 m 3 = 1 kL = 1 t (1000 kg) 1 dm 3 = 1 L = 1 kg 1 cm 3 = 1 mL = 1 g Mass of WaterVolume in Liters

27. Copyright © 2009 Pearson Education, Inc. 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.

28. Copyright © 2009 Pearson Education, Inc. Example: Capacity continued Solution: Since 1 m 3 of water = 1 kL of water, 0.156 m 3 = 0.156 kL, or 156 liters of water Since 1L = 1 kg, 156 L = 156 kg of water.

29. Copyright © 2009 Pearson Education, Inc. Temperature The term degrees Celsius (ºC) is used to measure temperature. Water boils212ºF100ºC Body temperature98.6ºF37ºC Comfortable room71.6ºF22ºC Water freezes32ºF0ºC Description ºFºC Temperature

30. Copyright © 2009 Pearson Education, Inc. Example: Choose ºF or ºC The temperature of a can of frozen juice about 2 __. The temperature of a person with a fever is about 101.5 __. The temperature of a bowl of hot soup is about 175 __. Solution: a) ºC b) ºF c) ºF

31. Copyright © 2009 Pearson Education, Inc. Conversions To covert from Celsius to Fahrenheit use the following formula. To covert from Fahrenheit to Celsius use the following formula.

32. Copyright © 2009 Pearson Education, Inc. Example: Conversions The air temperature on a warm summer day is about 85ºF. What is the equivalent temperature on the Celsius thermometer? Solution: The equivalent temperature is about 29.4ºC.

33. Copyright © 2009 Pearson Education, Inc. Example: Conversions The temperature of a cold glass of milk is about 5ºC. What is the equivalent temperature on the Fahrenheit thermometer? Solution: The equivalent temperature is about 41ºF.

34. Copyright © 2009 Pearson Education, Inc. 5.4 Dimensional Analysis and Conversions to and from the Metric System

35. Copyright © 2009 Pearson Education, Inc. 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:

36. Copyright © 2009 Pearson Education, Inc. U.S. Customary Units 1 pint = 2 cups 1 year = 365 days 1 cup (liquid) = 8 fluid ounces 1 day = 24 hours1 ton = 2000 pounds 1 hour = 60 minutes1 pound = 16 ounces 1 minute = 60 seconds1 mile = 5280 feet 1 gallon = 4 quarts1 yard = 3 feet 1 quart = 2 pints1 foot = 12 inches U.S. Customary Units

37. Copyright © 2009 Pearson Education, Inc. Example: Using Dimensional Analysis A recipe calls for 8 cups of blueberries. How many pints is this? Solution: Convert 75 miles per hour to inches per minute. Solution:

38. Copyright © 2009 Pearson Education, Inc. Conversion to and from the Metric System - Length LENGTH U.S. to Metric 1 inch (in.) ≈ 2.54 centimeters (cm) 1 foot (ft) ≈ 30 centimeters (cm) 1 yard (yd) ≈ 0.9 meter (m) 1 mile (mi) ≈ 1.6 kilometers (km)

39. Copyright © 2009 Pearson Education, Inc. Conversion to and from the Metric System - Area AREA U.S. to Metric 1 square inch (in. 2 ) ≈ 6.5 square centimeters (cm 2 ) 1 square foot (ft 2 ) ≈ 0.09 square meter (m 2 ) 1 square yard (yd 2 ) ≈ 0.8 square meter (m 2 ) 1 square mile (mi 2 ) ≈ 2.6 square kilometers (km 2 ) 1 acre ≈ 0.4 hectare (ha)

40. Copyright © 2009 Pearson Education, Inc. Conversion to and from the Metric System - Volume VOLUME U.S. to Metric 1 teaspoon (tsp) ≈ 5 milliliters (m l ) 1 tablespoon (tbsp) ≈ 15 milliliters (m l ) 1 fluid ounce (fl oz) ≈ 30 milliliters (m l ) 1 cup (c) ≈ 0.24 liter ( l ) 1 pint (pt) ≈ 0.47 liter ( l )

41. Copyright © 2009 Pearson Education, Inc. Conversion to and from the Metric System - Volume VOLUME U.S. to Metric 1 quart (qt) ≈ 0.95 liter ( l ) 1 gallon (gal) ≈ 3.8 liters ( l ) 1 cubic foot (ft 3 ) ≈ 0.03 cubic meter (m 3 ) 1 cubic yard (yd 3 ) ≈ 0.76 cubic meter (m 3 )

42. Copyright © 2009 Pearson Education, Inc. Conversion to and from the Metric System - Weight (Mass) WEIGHT OR MASS U.S. to Metric 1 ounce (oz) ≈ 28 grams (g) 1 pound (lb) ≈ 0.45 kilogram (kg) 1 ton (T) ≈ 0.9 tonne (t)

43. Copyright © 2009 Pearson Education, Inc. Example: Volume and Area A gas tank holds 22.6 gallons of gas. How many liters is this? Solution: The area of a box is 14.25 in 2. What is its area in square centimeters? Solution:

44. Copyright © 2009 Pearson Education, Inc. Example: Converting Speed A road in Toronto, Canada shows that the speed limit is 62 kph. Determine the speed in miles per hour. Solution: Since 62 km equals 38.75 mi, 62 kph is equivalent to 38.75 mph.

45. Copyright © 2009 Pearson Education, Inc. 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: The dosage of the medication is 73.92 mg.