Chapter 11: Measurement
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Transcript of Chapter 11: Measurement
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Chapter 11: Measurement
Section 11.1: Fundamentals of Measurement
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See Activity 11A regarding Measurable Attributes
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Structure of Measures
• Create an order (taller vs shorter, heavier vs lighter)
• Some are additive• Ex’s: length, weight, time• Non-Ex’s: temperature, density
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Definitions
•Def: unit- a reference amount for a given quantity
•Def: To measure a quantity- to compare that quantity with a unit of the quantity
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UnitsWhat makes a particular measurement a good choice as a unit?• Precise, standardized definition• Easy to convert to other units• Easily measurable
Some bad units:• Steps or paces• Square miles if measuring the size of a room
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Another bad unit• Lordes
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Standard U.S. System Units
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Deciding on which unit to useEx: Which unit would you use to measure the following?a) The area of this classroomb) The weight of a pencilc) The length of a basketball courtd) The volume of a water bottlee) The volume of a textbook
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The Units for the Metric System
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Metric System Prefixes
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Definitions of metric units•meter- originally defined as the length of a pendulum whose
half-period is exactly 1 second, or as 1/10,000,000 of the distance from the equator to the North Pole
• cc- cubic centimeter, used for dosages
•metric ton- 1000 kilograms
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Important relationships among metric units
•1 milliliter of water weighs 1 gram• No easy comparison for number of ounces a fluid ounce of water
weighs
•1 milliliter of liquid fills a 1 cubic centimeter container• No easy comparison for fluid ounces and cubic inches
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Converting between U.S. and metric systems• Length: 1 inch = 2.54 cm
• Capacity: 1 gallon ≈ 3.79 liters
• Weight/mass: 1 kg ≈ 2.2 pounds
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Measuring Length• How do we measure length?
Line units up end to end and count how many units make upthe quantity’s length
• What if the object isn’t straight?Run a string along the object or surface then measure the string’s length when it is straightened out
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Section 11.2: Length, Area, Volume, and Dimension
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Length• Def: Length- describes the size of something that is one-dimensional -
equal to the number of a chosen unit of length that it takes to cover the object without gaps or overlaps
• Def: one-dimensional- an object where at each point, there is only one independent direction to move within the object• Ex’s: line segment outer edge of a circle or polygon curved line equator of the Earth imaginary line from one end of a 2 or 3-dimensional object to the other end
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Perimeter• Def: The perimeter is the “distance around a shape,” or the length of
the outer edge of a shape.• Ex 1: How many feet of baseboard do you need to go around the
following room?
Assume each square in the grid is 1 square foot.
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Perimeter• Def: The perimeter is the “distance around a shape,” or the length of
the outer edge of a shape.• Ex 1: How many feet of baseboard do you need to go around the
following room?
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Area• Def: Area- describes the size of a two-dimensional object
- equal to the number of a chosen unit of area that it takes to cover the object without gaps or overlaps
• Def: 2-dimensional- at each point, there are 2 independent directions to go within the object • Ex’s: coordinate plane inside of a circle or polygon piece of paper surface of a box land surface of the Earth
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Example Area Problem• Ex 2: How many square feet of carpet do you need to cover the floor
of the following room?
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Example Area Problem• Ex 2: How many square feet of carpet do you need to cover the floor
of the following room?
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Volume• Def: Volume- describes the size of a 3-dimensional object
- equal to the number of a chosen unit of volume that it takes to fill the object without gaps or overlap
• Def: 3-dimensional- at each point, there are 3 independent directions to go within the object• Ex’s: atmosphere
inside of a balloon or box water in a container the Earth
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Example Volume Problem• Ex 3: How many cubic feet of air is in the following room if the flat
ceiling is 10 feet from the floor?
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Section 11.3: Error and Precision in Measurements
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Example Error Problem
• Ex 1: If a car company lists its sedan as weighing 3110 lbs, what could the car’s actual weight be?
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Another Example Problem
• Ex 2: If Colorado is reported to be 380 miles wide and 280 miles long, how large can the error be if the area is reported as 106,400 square miles?
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Section 11.4: Converting Between
Units of Measurement
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Converting Units
• Ex 1: A scale measures a dog’s weight to be 356 ounces. How many pounds does the dog weigh?
(Recall that )
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Converting Units• Def: Dimensional Analysis: process for converting between units by
multiplying the number 1 expressed as a fraction that relates two units
• Ex 2: How many miles are in 5 kilometers? (Recall that )
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See practice problems on Activity 11G
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Converting Units of Area and Volume
• Ex 3: Paulene is making a quilt which is made with patterned squares of size How many square pieces does she need to sew together to make the quilt?
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See more practice problems in Activity 11I
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Approximate Conversions
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Using Approximate Conversions
• Ex 4: Gas in England is currently and in the U.S. it is per gallon. In which country is gas cheaper?