{"id":200,"date":"2017-08-23T09:56:11","date_gmt":"2017-08-23T09:56:11","guid":{"rendered":"http:\/\/americanboard.org\/Subjects\/mathematics\/?page_id=200"},"modified":"2017-09-13T07:50:43","modified_gmt":"2017-09-13T07:50:43","slug":"about-measurement","status":"publish","type":"page","link":"https:\/\/americanboard.org\/Subjects\/mathematics\/about-measurement\/","title":{"rendered":"About Measurement"},"content":{"rendered":"<div class=\"twelve columns\" style=\"margin-top: 10%;\">\n<div class=\"advance\"><!--<a href=\"http:\/\/americanboard.org\/Subjects\/mathematics\/math_04_15.html\" class=\"button button-primary\">\u2b05 Previous Lesson<\/a>--><br \/>\n<a class=\"button\" href=\"http:\/\/americanboard.org\/Subjects\/mathematics\/measurement-and-linear-algebra\">Workshop Index<\/a>\u00a0<a class=\"button button-primary\" href=\"http:\/\/americanboard.org\/Subjects\/mathematics\/measuring-two-dimensional-figures\">Next Lesson \u27a1<\/a><\/div>\n<p><!-- CONTENT BEGINS HERE --><\/p>\n<h1 id=\"title\">About Measurement<\/h1>\n<h4>Objective<\/h4>\n<p>This lesson explores the nature of measurement and considers different units used for measuring. In this lesson, you\u00a0will learn to use composite measures and how to convert between different types of measures.<\/p>\n<h4>Previously Covered:<\/h4>\n<ul>\n<li>Measurement is a way that we\u00a0quantify amounts to express sizes, weights, and volumes, based\u00a0upon a certain standard.<\/li>\n<li>It is impossible to measure exactly because all measures\u00a0have a certain margin of error. For instance, if you measure the\u00a0length of a pencil with a 12-inch ruler, you will probably be\u00a0accurate to within an eighth of an inch.<\/li>\n<\/ul>\n<section>\n<h3>How do you choose the right unit for measurement?<\/h3>\n<p>There are myriad units for measuring, such as inches, ounces,\u00a0hours, cups, kilometers, amps, and bushels. Some units are\u00a0products of two measures such as foot-pounds. Other units are\u00a0ratios of two measures such as miles per hour, threads per inch,\u00a0dollars per gallon, people per square mile, and furlongs per\u00a0fortnight.<\/p>\n<p>Because there are so many units of measurement to choose from,\u00a0it is important that we know how to choose the appropriate unit to\u00a0use for a particular measurement. One thing we must consider in\u00a0choosing a unit to measure length, area, or volume is the number\u00a0of dimensions the item being measured has. The measurement unit\u00a0must have the same number of dimensions as the item. For instance,\u00a0area of a rectangle uses two dimensions: length and width, so it\u00a0needs a two-dimensional measurement unit, such as square\u00a0centimeters.<\/p>\n<h4><strong>Length <\/strong><\/h4>\n<p>Length is 1 dimension. Some of the common units used to measure length are inches, miles, centimeters, meters, feet, kilometers,\u00a0yards, and millimeters.<\/p>\n<h4><strong>Area <\/strong><\/h4>\n<p>Area has 2 dimensions (length and width). Some of the common\u00a0units used to measure area are square inches, square miles, square\u00a0centimeters, square meters, square feet, square kilometers, square\u00a0yards, and square millimeters.<\/p>\n<h4><strong>Volume <\/strong><\/h4>\n<p>Volume has 3 dimensions (length, width, and height). Some of\u00a0the common units used to measure volume are cubic inches, cubic\u00a0miles, cubic centimeters, cubic meters, cubic feet, cubic\u00a0kilometers, cubic yards, and cubic millimeters.<\/p>\n<section class=\"question\">\n<h4>Question<\/h4>\n<div>\n<p>The surface area of a cylinder could be measured in what units?<\/p>\n<ol>\n<li>Cubic centimeters<\/li>\n<li>Inches<\/li>\n<li>Ounces<\/li>\n<li>Square feet<\/li>\n<\/ol>\n<\/div>\n<p><a class=\"button button-primary q-answer\"> Reveal Answer <\/a><\/p>\n<div class=\"q-reveal\">\n<p>The correct choice is D. The surfaces of a cylinder are\u00a0two-dimensional, so they are measured in two-dimensional, or\u00a0square, units. Only choice D offers a square unit &#8211; square feet.<\/p>\n<\/div>\n<\/section>\n<p>How do you convert from one unit of measure to another?<\/p>\n<p>There are a number of ways to convert between units. One common\u00a0method of conversion is called <abbr title=\" a method of converting to equivalent units using ratios of equal amounts\">unit\u00a0analysis<\/abbr>. This process uses ratios and the cancellation\u00a0properties evidenced in fraction multiplication. Simply put, unit\u00a0analysis is nothing more than multiplication by forms of the\u00a0number 1. Multiplying a quantity by 1 does not change its value,\u00a0so we repeatedly multiply our original quantity by ratios, each of\u00a0which is equivalent to 1. We select the particular ratios to use\u00a0in such a way that the undesired units will appear in both the \u00a0numerator and denominator and cancel, leaving us with a string of\u00a0numbers which we can then multiply.\u00a0To perform unit analysis, you will need to know some <abbr title=\"conversion factors\">unit\u00a0equivalen<span style=\"text-decoration: none;\">ts<\/span><strong><span style=\"text-decoration: none;\">.<\/span><\/strong><\/abbr><\/p>\n<p class=\"white_lesson_header\" align=\"CENTER\">Unit Equivalents<\/p>\n<p>1 mile = 5,280 feet<\/p>\n<p>1 meter = 100 centimeters<\/p>\n<p>1 quart = 4 cups<\/p>\n<p>1 yard = 3 feet<\/p>\n<p>1 kilometer = 1,000 meters<\/p>\n<p>1 cup = 8 ounces<\/p>\n<p>1 foot = 12 inches<\/p>\n<p>1 kilogram = 1,000 grams<\/p>\n<p>1 ounce = 2 tablespoons<\/p>\n<p>1 inch = 2.54 centimeters<\/p>\n<p>1 gallon = 4 quarts<\/p>\n<p>1 tablespoon = 3 teaspoons<\/p>\n<h3>Converting Units<\/h3>\n<h4>What is 25 miles per hour converted to centimeters per second?<\/h4>\n<p>Convert the units using ratios of equivalent quantities.\u00a0Because we set up each ratio so that it is equal to one, the\u00a0amount being measured will stay the same, only the standard by\u00a0which we quantify that amount will change. Keep your eye on\u00a0reducing the units so that you end with your goal of centimeters\u00a0per second.<\/p>\n<p align=\"CENTER\"><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/americanboard.org\/Subjects\/Images\/math\/5\/s1_p3_html_669fccf0.gif\" width=\"487\" height=\"41\" name=\"graphics3\" align=\"BOTTOM\" border=\"0\" \/><\/p>\n<p align=\"CENTER\"><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/americanboard.org\/Subjects\/Images\/math\/5\/s1_p3_html_18df298f.gif\" width=\"512\" height=\"48\" name=\"graphics4\" align=\"BOTTOM\" border=\"0\" \/><\/p>\n<p>Multiplying the fractions together will converts 25 miles per\u00a0hour to 1,117.6 centimeters per second.<\/p>\n<section class=\"question\">\n<h4>Question<\/h4>\n<div>\n<p>A car traveling at the rate of 75 miles per hour is traveling\u00a0how many feet per second?<\/p>\n<ol>\n<li>54,000<\/li>\n<li>375<\/li>\n<li>238<\/li>\n<li>110<\/li>\n<\/ol>\n<\/div>\n<p><a class=\"button button-primary q-answer\"> Reveal Answer <\/a><\/p>\n<div class=\"q-reveal\">\n<p>The correct choice is D.<\/p>\n<p align=\"CENTER\"><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/americanboard.org\/Subjects\/Images\/math\/5\/s1_p3_html_6c519669.gif\" width=\"385\" height=\"41\" name=\"graphics5\" align=\"BOTTOM\" border=\"0\" \/><\/p>\n<\/div>\n<\/section>\n<section class=\"question\">\n<h4>Question<\/h4>\n<div>\n<p>If gasoline costs $2.79 per gallon, about how many ounces can\u00a0you buy for a penny?<\/p>\n<ol>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/americanboard.org\/Subjects\/Images\/math\/5\/images\/s1_p3_clip_image012.gif\" width=\"16\" height=\"41\" name=\"graphics6\" align=\"BOTTOM\" border=\"0\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/americanboard.org\/Subjects\/Images\/math\/5\/images\/s1_p3_clip_image015.gif\" width=\"16\" height=\"41\" name=\"graphics7\" align=\"BOTTOM\" border=\"0\" \/><\/li>\n<li>1<\/li>\n<li>2<\/li>\n<\/ol>\n<\/div>\n<p><a class=\"button button-primary q-answer\"> Reveal Answer <\/a><\/p>\n<div class=\"q-reveal\">\n<p>The correct choice is B.<\/p>\n<p align=\"CENTER\"><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/americanboard.org\/Subjects\/Images\/math\/5\/s1_p3_html_4e8639c1.gif\" width=\"639\" height=\"44\" name=\"graphics8\" align=\"BOTTOM\" border=\"0\" \/><\/p>\n<\/div>\n<\/section>\n<h3>Review of New Vocabulary and Concepts<\/h3>\n<ul>\n<li>measurement unit\u00a0must have the same number of dimensions as the quality being\u00a0measured.<\/li>\n<li>The unit of measurement can be <strong><em>converted\u00a0<\/em><\/strong>by multiplying the measurement by ratios of equivalent units and\u00a0reducing those units, just as you do in fraction multiplication.<\/li>\n<\/ul>\n<\/section>\n<p><!-- CONTENT ENDS HERE --><\/p>\n<div class=\"advance\"><!--<a href=\"http:\/\/americanboard.org\/Subjects\/mathematics\/math_04_15.html\" class=\"button button-primary\">\u2b05 Previous Lesson<\/a>--><br \/>\n<a class=\"button\" href=\"http:\/\/americanboard.org\/Subjects\/mathematics\/measurement-and-linear-algebra\">Workshop Index<\/a>\u00a0<a class=\"button button-primary\" href=\"http:\/\/americanboard.org\/Subjects\/mathematics\/measuring-two-dimensional-figures\">Next Lesson \u27a1<\/a><\/div>\n<p><a class=\"backtotop\" href=\"#title\">Back to Top<\/a><\/p>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Workshop Index\u00a0Next Lesson \u27a1 About Measurement Objective This lesson explores the nature of measurement and considers different units used for measuring. In this lesson, you\u00a0will learn to use composite measures and how to convert between different types of measures. Previously Covered: Measurement is a way that we\u00a0quantify amounts to express sizes, weights, and volumes, based\u00a0upon [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-200","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/americanboard.org\/Subjects\/mathematics\/wp-json\/wp\/v2\/pages\/200","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/americanboard.org\/Subjects\/mathematics\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/americanboard.org\/Subjects\/mathematics\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/americanboard.org\/Subjects\/mathematics\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/americanboard.org\/Subjects\/mathematics\/wp-json\/wp\/v2\/comments?post=200"}],"version-history":[{"count":6,"href":"https:\/\/americanboard.org\/Subjects\/mathematics\/wp-json\/wp\/v2\/pages\/200\/revisions"}],"predecessor-version":[{"id":695,"href":"https:\/\/americanboard.org\/Subjects\/mathematics\/wp-json\/wp\/v2\/pages\/200\/revisions\/695"}],"wp:attachment":[{"href":"https:\/\/americanboard.org\/Subjects\/mathematics\/wp-json\/wp\/v2\/media?parent=200"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}