1. Chapter 8 Section 4 - Slide 1 Copyright © 2009 Pearson Education, Inc. AND

2. Copyright © 2009 Pearson Education, Inc. Chapter 8 Section 4 - Slide 2 Chapter 8 The Metric System

3. Copyright © 2009 Pearson Education, Inc. Chapter 8 Section 4 - Slide 3 WHAT YOU WILL LEARN Dimensional analysis and converting to and from the metric system

4. Copyright © 2009 Pearson Education, Inc. Chapter 8 Section 4 - Slide 4 Section 4 Dimensional Analysis and Conversions to and from the Metric System

5. Chapter 8 Section 4 - Slide 5 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:

6. Chapter 8 Section 4 - Slide 6 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

7. Chapter 8 Section 4 - Slide 7 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:

8. Chapter 8 Section 4 - Slide 8 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)

9. Chapter 8 Section 4 - Slide 9 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)

10. Chapter 8 Section 4 - Slide 10 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 )

11. Chapter 8 Section 4 - Slide 11 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 )

12. Chapter 8 Section 4 - Slide 12 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)

13. Chapter 8 Section 4 - Slide 13 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:

14. Chapter 8 Section 4 - Slide 14 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.

15. Chapter 8 Section 4 - Slide 15 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 baby’s weight, what dosage should be given? Solution: The dosage of the medication is 73.92 mg.

16. Copyright © 2009 Pearson Education, Inc. Chapter 8 Section 4 - Slide 16 Chapter 9 Geometry

17. Copyright © 2009 Pearson Education, Inc. Chapter 8 Section 4 - Slide 17 WHAT YOU WILL LEARN Perimeter and area

18. Copyright © 2009 Pearson Education, Inc. Chapter 8 Section 4 - Slide 18 Section 3 Perimeter and Area

19. Chapter 8 Section 4 - Slide 19 Copyright © 2009 Pearson Education, Inc. Formulas P = s 1 + s 2 + b 1 + b 2 P = s 1 + s 2 + s 3 P = 2b + 2w P = 4s P = 2l + 2w Perimeter Trapezoid Triangle A = bhParallelogram A = s 2 Square A = lwRectangle AreaFigure

20. Chapter 8 Section 4 - Slide 20 Copyright © 2009 Pearson Education, Inc. Example Marcus Sanderson needs to put a new roof on his barn. One square of roofing covers 100 ft 2 and costs $32.00 per square. If one side of the barn roof measures 50 feet by 30 feet, determine a) the area of the entire roof. b) how many squares of roofing he needs. c) the cost of putting on the roof. side 1 side 2 Roof

21. Chapter 8 Section 4 - Slide 21 Copyright © 2009 Pearson Education, Inc. Example (continued) a) The area of one side of the roof is A = lw A = 30 ft  50 ft A = 1500 ft 2 Both sides of the roof = 1500 ft 2  2 = 3000 ft 2 b) Determine the number of squares

22. Chapter 8 Section 4 - Slide 22 Copyright © 2009 Pearson Education, Inc. Example (continued) c) Determine the cost 30 squares  $32 per square $960 It will cost a total of $960 to roof the barn.

23. Chapter 8 Section 4 - Slide 23 Copyright © 2009 Pearson Education, Inc. Pythagorean Theorem The sum of the squares of the lengths of the legs of a right triangle equals the square of the length of the hypotenuse. leg 2 + leg 2 = hypotenuse 2 Symbolically, if a and b represent the lengths of the legs and c represents the length of the hypotenuse (the side opposite the right angle), then a 2 + b 2 = c 2 a b c

24. Chapter 8 Section 4 - Slide 24 Copyright © 2009 Pearson Education, Inc. Example Tomas is bringing his boat into a dock that is 12 feet above the water level. If a 38 foot rope is attached to the dock on one side and to the boat on the other side, determine the horizontal distance from the dock to the boat. 12 ft 38 ft rope

25. Chapter 8 Section 4 - Slide 25 Copyright © 2009 Pearson Education, Inc. Example (continued) The distance is approximately 36.06 feet. 12 38 b

26. Chapter 8 Section 4 - Slide 26 Copyright © 2009 Pearson Education, Inc. Circles A circle is a set of points equidistant from a fixed point called the center. A radius, r, of a circle is a line segment from the center of the circle to any point on the circle. A diameter, d, of a circle is a line segment through the center of the circle with both end points on the circle. The circumference is the length of the simple closed curve that forms the circle. d r circumference

27. Chapter 8 Section 4 - Slide 27 Copyright © 2009 Pearson Education, Inc. Example Terri is installing a new circular swimming pool in her backyard. The pool has a diameter of 27 feet. How much area will the pool take up in her yard? (Use π = 3.14.) The radius of the pool is 13.5 ft. The pool will take up about 572 square feet.