{"id":68,"date":"2023-01-25T16:33:59","date_gmt":"2023-01-25T16:33:59","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/chapter\/us-units-of-measurement-learn-it-page-5\/"},"modified":"2026-02-11T21:19:38","modified_gmt":"2026-02-11T21:19:38","slug":"us-units-of-measurement-learn-it-5","status":"web-only","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/chapter\/us-units-of-measurement-learn-it-5\/","title":{"raw":"US Units of Measurement: Learn It 5","rendered":"US Units of Measurement: Learn It 5"},"content":{"raw":"<h2>Capacity<\/h2>\r\n<p><iframe src=\"https:\/\/lumenlearning.h5p.com\/content\/1291931939946215658\/embed\" width=\"1088\" height=\"637\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\" aria-label=\"Capacity Interactive\"><\/iframe><script src=\"https:\/\/lumenlearning.h5p.com\/js\/h5p-resizer.js\" charset=\"UTF-8\"><\/script><\/p>\r\n<section class=\"textbox keyTakeaway\">\r\n<div>\r\n<h3>units of capacity<\/h3>\r\n<p style=\"text-align: left;\"><b>Capacity<\/b> is the amount of liquid (or other pourable substance) that an object can hold when it\u2019s full. There are five main units for measuring capacity in the U.S. customary measurement system - <b>fluid ounce<\/b>, <b>cup<\/b>, <b>pint<\/b>, <b>quart<\/b>, and <b>gallon<\/b>.<\/p>\r\n<p style=\"text-align: center;\">\u00a0<\/p>\r\n<table class=\"aligncenter\" style=\"border-spacing: 0px; width: 74.8726%;\" border=\"1\" cellpadding=\"0\">\r\n<tbody>\r\n<tr>\r\n<td style=\"text-align: center; width: 20%;\"><b>Unit Equivalents<\/b><\/td>\r\n<td style=\"text-align: center; width: 40%;\"><b>Conversion Factors (bigger to smaller units of measurement)<\/b><\/td>\r\n<td style=\"text-align: center; width: 40%;\"><b>Conversion Factors (smaller to bigger units of measurement)<\/b><\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"text-align: center; width: 20%;\">[latex]1[\/latex] cup = [latex]8[\/latex] fluid ounces<\/td>\r\n<td style=\"text-align: center; width: 40%;\">[latex] \\displaystyle \\frac{\\text{8 fluid ounces}}{\\text{1 cup}}[\/latex]<\/td>\r\n<td style=\"text-align: center; width: 40%;\">[latex] \\displaystyle \\frac{\\text{1 cup}}{\\text{8 fluid ounces}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"text-align: center; width: 20%;\">[latex]1[\/latex] pint = [latex]2[\/latex] cups<\/td>\r\n<td style=\"text-align: center; width: 40%;\">[latex] \\displaystyle \\frac{2\\text{ cups}}{1\\text{ pint}}[\/latex]<\/td>\r\n<td style=\"text-align: center; width: 40%;\">[latex] \\displaystyle \\frac{\\text{1 pint}}{2\\text{ cups}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"text-align: center; width: 20%;\">[latex]1[\/latex] quart = [latex]2[\/latex] pints<\/td>\r\n<td style=\"text-align: center; width: 40%;\">[latex] \\displaystyle \\frac{2\\text{ pints}}{\\text{1 quart}}[\/latex]<\/td>\r\n<td style=\"text-align: center; width: 40%;\">[latex] \\displaystyle \\frac{\\text{1 quart}}{2\\text{ pints}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"text-align: center; width: 20%;\">[latex]1[\/latex] quart = [latex]4[\/latex] cups<\/td>\r\n<td style=\"text-align: center; width: 40%;\">[latex] \\displaystyle \\frac{4\\text{ cups}}{\\text{1 quart}}[\/latex]<\/td>\r\n<td style=\"text-align: center; width: 40%;\">[latex] \\displaystyle \\frac{\\text{1 quart}}{4\\text{ cups}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"text-align: center; width: 20%;\">[latex]1[\/latex] gallon = [latex]4[\/latex] quarts<\/td>\r\n<td style=\"text-align: center; width: 40%;\">[latex] \\displaystyle \\frac{4\\text{ quarts}}{\\text{1 gallon}}[\/latex]<\/td>\r\n<td style=\"text-align: center; width: 40%;\">[latex] \\displaystyle \\frac{\\text{1 gallon}}{4\\text{ quarts}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"text-align: center; width: 20%;\">[latex]1[\/latex] gallon = [latex]16[\/latex] cups<\/td>\r\n<td style=\"text-align: center; width: 40%;\">[latex] \\displaystyle \\frac{\\text{16 cups}}{1\\text{ gallon}}[\/latex]<\/td>\r\n<td style=\"text-align: center; width: 40%;\">[latex] \\displaystyle \\frac{1\\text{ gallon}}{\\text{16 cups}}[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<\/section>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]1879[\/ohm2_question]<\/section>\r\n<p>Sometimes you will need to convert between units of measurement. For example, you might want to express [latex]5[\/latex] gallons of lemonade in cups if you are trying to determine how many [latex]8[\/latex] fluid ounce servings the amount of lemonade would yield. As with converting units of length and weight, you can use the factor label method to convert from one unit of capacity to another.<\/p>\r\n<section class=\"textbox example\">How many pints is [latex] \\displaystyle 2\\frac{3}{4}[\/latex] gallons?<br \/>\r\n[reveal-answer q=\"442206\"]Show Solution[\/reveal-answer]<br \/>\r\n[hidden-answer a=\"442206\"]Begin by reasoning about your answer. Since a gallon is larger than a pint, expect the answer in pints to be a number greater than [latex] \\displaystyle 2\\frac{3}{4}[\/latex].\r\n\r\n<p style=\"text-align: center;\">[latex]2\\frac{3}{4}\\text{ gallons}=\\text{___ pints}[\/latex]<\/p>\r\n<p>The table above does not contain a conversion factor for gallons and pints, so you cannot convert it in one step. However, you can use quarts as an intermediate unit, as shown here.<\/p>\r\n<p>Set up the equation so that two sets of labels cancel: gallons and quarts.<\/p>\r\n<p style=\"text-align: center;\">[latex]\\frac{11\\text{ gallons}}{4}\\cdot\\frac{4\\text{ quarts}}{1\\text{ gallon}}\\cdot\\frac{2\\text{ pints}}{1\\text{ quart}}=\\text{___ pints}[\/latex]<\/p>\r\n<p style=\"text-align: center;\">[latex]\\frac{11\\cancel{\\text{ gallons}}}{4}\\cdot\\frac{4\\cancel{\\text{ quarts}}}{1\\cancel{\\text{ gallon}}}\\cdot\\frac{2\\text{ pints}}{1\\cancel{\\text{ quart}}}=\\text{___ pints}[\/latex]<\/p>\r\n<p style=\"text-align: center;\">\u00a0[latex]\\frac{11}{4}\\cdot\\frac{4}{1}\\cdot\\frac{2\\text{ pints}}{1}=\\text{___ pints}[\/latex]<\/p>\r\n<p>Multiply and simplify.<\/p>\r\n<p style=\"text-align: center;\">[latex]\\frac{11\\cdot4\\cdot2\\text{ pints}}{4\\cdot1\\cdot1}=\\text{___ pints}[\/latex]<\/p>\r\n<p style=\"text-align: center;\">[latex]\\frac{88\\text{ pints}}{4}=22\\text{ pints}[\/latex]<\/p>\r\n<p>[latex] \\displaystyle 2\\frac{3}{4}[\/latex] gallons is [latex]22[\/latex] pints.<\/p>\r\n<p>[\/hidden-answer]<\/p>\r\n<\/section>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]1878[\/ohm2_question]<\/section>","rendered":"<h2>Capacity<\/h2>\n<p><iframe loading=\"lazy\" src=\"https:\/\/lumenlearning.h5p.com\/content\/1291931939946215658\/embed\" width=\"1088\" height=\"637\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\" aria-label=\"Capacity Interactive\"><\/iframe><script src=\"https:\/\/lumenlearning.h5p.com\/js\/h5p-resizer.js\" charset=\"UTF-8\"><\/script><\/p>\n<section class=\"textbox keyTakeaway\">\n<div>\n<h3>units of capacity<\/h3>\n<p style=\"text-align: left;\"><b>Capacity<\/b> is the amount of liquid (or other pourable substance) that an object can hold when it\u2019s full. There are five main units for measuring capacity in the U.S. customary measurement system &#8211; <b>fluid ounce<\/b>, <b>cup<\/b>, <b>pint<\/b>, <b>quart<\/b>, and <b>gallon<\/b>.<\/p>\n<p style=\"text-align: center;\">\u00a0<\/p>\n<table class=\"aligncenter\" style=\"border-spacing: 0px; width: 74.8726%;\" cellpadding=\"0\">\n<tbody>\n<tr>\n<td style=\"text-align: center; width: 20%;\"><b>Unit Equivalents<\/b><\/td>\n<td style=\"text-align: center; width: 40%;\"><b>Conversion Factors (bigger to smaller units of measurement)<\/b><\/td>\n<td style=\"text-align: center; width: 40%;\"><b>Conversion Factors (smaller to bigger units of measurement)<\/b><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center; width: 20%;\">[latex]1[\/latex] cup = [latex]8[\/latex] fluid ounces<\/td>\n<td style=\"text-align: center; width: 40%;\">[latex]\\displaystyle \\frac{\\text{8 fluid ounces}}{\\text{1 cup}}[\/latex]<\/td>\n<td style=\"text-align: center; width: 40%;\">[latex]\\displaystyle \\frac{\\text{1 cup}}{\\text{8 fluid ounces}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center; width: 20%;\">[latex]1[\/latex] pint = [latex]2[\/latex] cups<\/td>\n<td style=\"text-align: center; width: 40%;\">[latex]\\displaystyle \\frac{2\\text{ cups}}{1\\text{ pint}}[\/latex]<\/td>\n<td style=\"text-align: center; width: 40%;\">[latex]\\displaystyle \\frac{\\text{1 pint}}{2\\text{ cups}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center; width: 20%;\">[latex]1[\/latex] quart = [latex]2[\/latex] pints<\/td>\n<td style=\"text-align: center; width: 40%;\">[latex]\\displaystyle \\frac{2\\text{ pints}}{\\text{1 quart}}[\/latex]<\/td>\n<td style=\"text-align: center; width: 40%;\">[latex]\\displaystyle \\frac{\\text{1 quart}}{2\\text{ pints}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center; width: 20%;\">[latex]1[\/latex] quart = [latex]4[\/latex] cups<\/td>\n<td style=\"text-align: center; width: 40%;\">[latex]\\displaystyle \\frac{4\\text{ cups}}{\\text{1 quart}}[\/latex]<\/td>\n<td style=\"text-align: center; width: 40%;\">[latex]\\displaystyle \\frac{\\text{1 quart}}{4\\text{ cups}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center; width: 20%;\">[latex]1[\/latex] gallon = [latex]4[\/latex] quarts<\/td>\n<td style=\"text-align: center; width: 40%;\">[latex]\\displaystyle \\frac{4\\text{ quarts}}{\\text{1 gallon}}[\/latex]<\/td>\n<td style=\"text-align: center; width: 40%;\">[latex]\\displaystyle \\frac{\\text{1 gallon}}{4\\text{ quarts}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center; width: 20%;\">[latex]1[\/latex] gallon = [latex]16[\/latex] cups<\/td>\n<td style=\"text-align: center; width: 40%;\">[latex]\\displaystyle \\frac{\\text{16 cups}}{1\\text{ gallon}}[\/latex]<\/td>\n<td style=\"text-align: center; width: 40%;\">[latex]\\displaystyle \\frac{1\\text{ gallon}}{\\text{16 cups}}[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm1879\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=1879&theme=lumen&iframe_resize_id=ohm1879&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<p>Sometimes you will need to convert between units of measurement. For example, you might want to express [latex]5[\/latex] gallons of lemonade in cups if you are trying to determine how many [latex]8[\/latex] fluid ounce servings the amount of lemonade would yield. As with converting units of length and weight, you can use the factor label method to convert from one unit of capacity to another.<\/p>\n<section class=\"textbox example\">How many pints is [latex]\\displaystyle 2\\frac{3}{4}[\/latex] gallons?<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><button class=\"show-answer show-answer-button collapsed\" data-target=\"q442206\">Show Solution<\/button><\/p>\n<div id=\"q442206\" class=\"hidden-answer\" style=\"display: none\">Begin by reasoning about your answer. Since a gallon is larger than a pint, expect the answer in pints to be a number greater than [latex]\\displaystyle 2\\frac{3}{4}[\/latex].<\/p>\n<p style=\"text-align: center;\">[latex]2\\frac{3}{4}\\text{ gallons}=\\text{___ pints}[\/latex]<\/p>\n<p>The table above does not contain a conversion factor for gallons and pints, so you cannot convert it in one step. However, you can use quarts as an intermediate unit, as shown here.<\/p>\n<p>Set up the equation so that two sets of labels cancel: gallons and quarts.<\/p>\n<p style=\"text-align: center;\">[latex]\\frac{11\\text{ gallons}}{4}\\cdot\\frac{4\\text{ quarts}}{1\\text{ gallon}}\\cdot\\frac{2\\text{ pints}}{1\\text{ quart}}=\\text{___ pints}[\/latex]<\/p>\n<p style=\"text-align: center;\">[latex]\\frac{11\\cancel{\\text{ gallons}}}{4}\\cdot\\frac{4\\cancel{\\text{ quarts}}}{1\\cancel{\\text{ gallon}}}\\cdot\\frac{2\\text{ pints}}{1\\cancel{\\text{ quart}}}=\\text{___ pints}[\/latex]<\/p>\n<p style=\"text-align: center;\">\u00a0[latex]\\frac{11}{4}\\cdot\\frac{4}{1}\\cdot\\frac{2\\text{ pints}}{1}=\\text{___ pints}[\/latex]<\/p>\n<p>Multiply and simplify.<\/p>\n<p style=\"text-align: center;\">[latex]\\frac{11\\cdot4\\cdot2\\text{ pints}}{4\\cdot1\\cdot1}=\\text{___ pints}[\/latex]<\/p>\n<p style=\"text-align: center;\">[latex]\\frac{88\\text{ pints}}{4}=22\\text{ pints}[\/latex]<\/p>\n<p>[latex]\\displaystyle 2\\frac{3}{4}[\/latex] gallons is [latex]22[\/latex] pints.<\/p>\n<\/div>\n<\/div>\n<\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm1878\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=1878&theme=lumen&iframe_resize_id=ohm1878&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n","protected":false},"author":15,"menu_order":8,"template":"","meta":{"_candela_citation":"[]","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"part":62,"module-header":"learn_it","content_attributions":[],"internal_book_links":[],"video_content":null,"cc_video_embed_content":{"cc_scripts":"","media_targets":[]},"try_it_collection":null,"_links":{"self":[{"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/pressbooks\/v2\/chapters\/68"}],"collection":[{"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/wp\/v2\/users\/15"}],"version-history":[{"count":23,"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/pressbooks\/v2\/chapters\/68\/revisions"}],"predecessor-version":[{"id":15994,"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/pressbooks\/v2\/chapters\/68\/revisions\/15994"}],"part":[{"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/pressbooks\/v2\/parts\/62"}],"metadata":[{"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/pressbooks\/v2\/chapters\/68\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/wp\/v2\/media?parent=68"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/pressbooks\/v2\/chapter-type?post=68"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/wp\/v2\/contributor?post=68"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/wp\/v2\/license?post=68"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}