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

AND

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

Chapter 8

The Metric System

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

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

Section 4

Dimensional Analysis and Conversions to and from the

Metric System

Chapter 8 Section 4 - Slide 5Copyright © 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:

16 oz

1 lb

1 hr

60 min

12 in.

1 ft

Chapter 8 Section 4 - Slide 6Copyright © 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

Chapter 8 Section 4 - Slide 7Copyright © 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 cups = 8 cups 1 pint

2 cups

4 pint s

75mi

hr 75

mi

hr

5280ft

1 mi

12 in

1 ft

1 hr

60 min

75 5280 12

60

in

min = 79,200

in

min

Chapter 8 Section 4 - Slide 8Copyright © 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)

Chapter 8 Section 4 - Slide 9Copyright © 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 (cm2)

1 square foot (ft2) ≈ 0.09 square meter (m2)

1 square yard (yd2) ≈ 0.8 square meter (m2)

1 square mile (mi2) ≈ 2.6 square kilometers (km2)

1 acre ≈ 0.4 hectare (ha)

Chapter 8 Section 4 - Slide 10Copyright © 2009 Pearson Education, Inc.

Conversion to and from the Metric System - Volume

VOLUME

U.S. to Metric

1 teaspoon (tsp) ≈ 5 milliliters (ml)

1 tablespoon (tbsp) ≈ 15 milliliters (ml)

1 fluid ounce (fl oz) ≈ 30 milliliters (ml)

1 cup (c) ≈ 0.24 liter (l)

1 pint (pt) ≈ 0.47 liter (l)

Chapter 8 Section 4 - Slide 11Copyright © 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 (ft3) ≈ 0.03 cubic meter (m3)

1 cubic yard (yd3) ≈ 0.76 cubic meter (m3)

Chapter 8 Section 4 - Slide 12Copyright © 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)

Chapter 8 Section 4 - Slide 13Copyright © 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 in2. What is its area in square centimeters?

Solution:

´ =3.8

22.6 gal 85.88 lgal

14.25 in2 6.5 cm2

1 in2

92.625 cm2

Chapter 8 Section 4 - Slide 14Copyright © 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.

62 km

1 mi

1.6 km

62

1.6mi 38.75 mi

Chapter 8 Section 4 - Slide 15Copyright © 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.

8 lbs 16 oz

1 lb

4 oz 128 oz 4 oz 132 oz

132 oz28 g

oz

1 kg

1000 g

20 mg

1 kg

73.92 mg

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

Chapter 9

Geometry

Copyright © 2009 Pearson Education, Inc. Chapter 8 Section 4 - Slide 17

WHAT YOU WILL LEARN

• Perimeter and area

Copyright © 2009 Pearson Education, Inc. Chapter 8 Section 4 - Slide 18

Section 3

Perimeter and Area

Chapter 8 Section 4 - Slide 19Copyright © 2009 Pearson Education, Inc.

Formulas

P = s1 + s2 + b1 + b2

P = s1 + s2 + s3

P = 2b + 2w

P = 4s

P = 2l + 2w

Perimeter

Trapezoid

Triangle

A = bhParallelogram

A = s2Square

A = lwRectangle

AreaFigure

12A bh

11 22 ( )A h b b

Chapter 8 Section 4 - Slide 20Copyright © 2009 Pearson Education, Inc.

Example Marcus Sanderson needs to put a new roof on his barn.

One square of roofing covers 100 ft2 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

Chapter 8 Section 4 - Slide 21Copyright © 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 ft2

Both sides of the roof = 1500 ft2 2 = 3000 ft2

b) Determine the number of squares

= =area of roof 3000sq. ft.

30area of one square 100sq. ft.

Chapter 8 Section 4 - Slide 22Copyright © 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.

Chapter 8 Section 4 - Slide 23Copyright © 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.

leg2 + leg2 = hypotenuse2

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

a2 + b2 = c2 a

b

c

Chapter 8 Section 4 - Slide 24Copyright © 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

Chapter 8 Section 4 - Slide 25Copyright © 2009 Pearson Education, Inc.

Example (continued)

The distance is approximately 36.06 feet.

+ =

+ =

+ =

=

=

»

2 2 2

2 2 2

2

2

12 38

144 1444

1300

1300

36.06

a b c

b

b

b

b

b

1238

b

Chapter 8 Section 4 - Slide 26Copyright © 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

Chapter 8 Section 4 - Slide 27Copyright © 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.)

A r 2

A (13.5)2

A 572.265

The radius of the pool is 13.5 ft.

The pool will take up about 572 square feet.