Chapter 11: Measurement Section 11.1: Fundamentals of Measurement

See Activity 11A regarding Measurable Attributes

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

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

Units What 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

Another bad unit Lordes

Standard U.S. System Units

Deciding on which unit to use Ex: Which unit would you use to measure the following? a)The area of this classroom b)The weight of a pencil c)The length of a basketball court d)The volume of a water bottle e)The volume of a textbook

The Units for the Metric System

Metric System Prefixes

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 kilograms

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

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

Measuring Length How do we measure length? Line units up end to end and count how many units make up the 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

Section 11.2: Length, Area, Volume, and Dimension

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

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.

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?

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

Example Area Problem Ex 2: How many square feet of carpet do you need to cover the floor of the following room?

Example Area Problem Ex 2: How many square feet of carpet do you need to cover the floor of the following room?

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

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?

Section 11.3: Error and Precision in Measurements

Example Error Problem Ex 1: If a car company lists its sedan as weighing 3110 lbs, what could the car’s actual weight be?

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?

Section 11.4: Converting Between Units of Measurement

Converting Units

See practice problems on Activity 11G

Converting Units of Area and Volume

See more practice problems in Activity 11I

Approximate Conversions

Using Approximate Conversions