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Chapter 10 Measurement Section 10.1 Systems of Measurement

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Measuring an object is to assign a number to a feature of it in some sort of standardized way. The way the number is assigned usually has several common properties. 1. The measurement number is never negative. 2. The measurement number being zero indicates none of what you are measuring is present. 3. The more of the feature you are measuring there is the larger the measurement number you assign. 4. A standard unit is used so that the measurement can be replicated. For example if you go to buy a pair of pants there are two features of the pants that a number has been assign to; the waist and the inseam. This is a positive number that matches the distance around your waist. A waist size of 32 is smaller than a waist size of 38. Features of Geometric Shapes and Physical Objects The features of geometrical shapes we will be interested in measuring are length, area and volume (capacity). The features of physical objects we will be interested in measuring are mass (weight) and temperature.

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Measuring Length To measure the length of a line segment you want to find how many unit segments laid end to end will be congruent to the segment you want to measure. The number of units that are used is the measure in that length of unit. Look at the example below of using red, green and orange units to measure the black segment. 1 Black Segment = 2 Red Segments = 4 Green Segments = 8 Orange Segments = Measurement Systems: English vs Metric The English system of measure based its lengths on certain objects or body parts. The common units that are used are: inch, foot, yard and mile. The metric system of measure based its lengths on the speed of light. The common units for it are: millimeter, centimeter, meter, kilometer.

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The units that are chosen by a child to measure (or approximate) a distance come from setting up benchmarks which are common measurements of things in the environment. For Example: The length of a standard size sheet of paper is about 1 foot. (The paper is a benchmark for 1 foot.) A football field is 100 yards long. (The football field is a benchmark for 100 yards.) A meter is about the length of my leg. (My leg is the benchmark for a meter.) A mile is about 17 football fields in length. (17 football fields are a benchmark for a mile.) Units for the English and Metric Systems English System 1 foot = 12 inches 1 yard = 3 feet 1 mile = 5280 feet Metric System – These prefixes and symbols are used with the metric system units: meters (m), grams (g) and liters (L). Prefixkilohectodeckadecicentimilli Symbolkhdkdcm Number

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Other Measurements Sometimes we wish to measure other qualities of an object (or person) besides length. Some of the other things that are measured include: Mass (weight) – units include: pounds, ounces, grams, kilograms Capacity (volume) – units include: ounces, cups, quarts, gallons, milliliters, liters Time – units include: seconds, minutes, hours, days, weeks, years, decades Temperature – units include: Fahrenheit, Celsius Unit Conversion To convert from one unit to another we use an idea called dimensional analysis or cancellation of units. You start with the units you have and on the other side of the equation you put the units you want to change to. You write down fraction or fractions with the correct units so they cancel and leave you with what is on the other side. For example if we wish to change 250 yards into miles. 250 yard = mile 3 feet 1 yard 1 mile 5280 feet = (250)(3) mile yards cancelfeet cancel

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40 hour Convert 40 hours into weeks. 1 day 24 hour 1 week 7 day =40 (24)(7) week = week cancel hours cancel days Precision The smaller a unit is the more precise it is (i.e. the more accurately you know the value of what you are trying to measure). For example yards are more accurate than miles. Feet are more accurate than yards. Inches are more precise than feet. Which of the following are more precise? about 31 inches orabout 2.5 feet

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