Chapter 13 (Sp12)

# Chapter 13 (Sp12) - Section 13-1 Linear Measure Units of...

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Section 13-1 – Linear Measure Units of Length in the English System : 1 yard = 3 feet = 36 inches 1 foot = 1 / 3 yard = 1 / 5280 mile 1 foot = 12 inches 1 inch = 1 / 12 foot = 1 / 36 yard = 1 / 63360 mile 1 mile = 1760 yards = 5280 feet 1 yard = 1 / 1760 mile We can convert from one unit of measure to another using “dimensional analysis” . Example : If a car is traveling at 65 miles per hour, what is its speed in feet per second? Example : Convert 5432 yards per minute into miles per hour Example : Convert 64 inches into yards Example : Convert 0.4 miles into feet. Example : Convert 0.875 feet into yards. 1

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The Metric System Unit Symbol Relationship to base unit Kilometer km 1000 m Hectometer hm 100 m Dekameter dam 10 m Meter m Base unit Decimeter dm 0.1 m Centimeter cm 0.01 m Millimeter mm 0.001 m Conversion Relationship (see pg. 843) Kilo 10 3 hecto 10 2 deka 10 1 base (unit)___ 10 0 deci 10 -1 centi 10 -2 milli 10 -3 Example : Convert the following a) 1.7 km into meters b) 385 mm into meters c) 0.08 km into centimeters d) 15 mm into centimeters 2
Distance Properties: 1. The distance between any two points A and B is greater than or equal to 0. (AB ≥ 0) 2. The distance between any two points A and B is the same as the distance between points B and A. (AB = BA) 3. For any three points A, B, and C, the distance between A and B plus the distance between B and C is greater than or equal to the distance between A and C (AB + BC ≥ AC) If A, B, and C are collinear and B is in between A and C, then AB + BC = AC. A B C If A, B, and C are NOT collinear (and form a triangle), then AB + BC > AC. This is known as the Triangle Inequality . B A C Example : Two sides of a triangle are 31 cm and 85 cm long and the measure of the third side must be measured in centimeters. a) What is the longest the third side can be? b) What is the shortest the third side can be? 3

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The perimeter of a simple closed curve is the length of the curve. Example : Find the perimeter of the following: a) A square with 5 mm sides. b) A rectangle with length 8 feet and width 3 feet. The perimeter of a circle is called circumference . In the late 18 th century, mathematicians proved that the ratio of circumference to diameter is pi. ie, So, C = _______________ or C = __________________ Example : Find the circumference of a circle with : a) A diameter of 12 inches b) A radius of 0.5 cm. Example: If the circumference of a circle is 20π ft, what is the radius of the circle? 4
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Chapter 13 (Sp12) - Section 13-1 Linear Measure Units of...

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