{"id":9658,"date":"2017-05-03T20:44:21","date_gmt":"2017-05-03T20:44:21","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/prealgebra\/?post_type=chapter&#038;p=9658"},"modified":"2024-04-30T21:21:42","modified_gmt":"2024-04-30T21:21:42","slug":"summary-classes-of-real-numbers","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/wm-developmentalemporium\/chapter\/summary-classes-of-real-numbers\/","title":{"raw":"Summary: Classes of Real Numbers","rendered":"Summary: Classes of Real Numbers"},"content":{"raw":"<h2>Key Concepts<\/h2>\r\n<ul id=\"eip-693\">\r\n \t<li><strong>Real numbers<\/strong><\/li>\r\n<\/ul>\r\n<img class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24222311\/CNX_BMath_Figure_07_01_001.png\" alt=\"The image shows a large rectangle labeled \u201cReal Numbers\u201d. The rectangle is split in half vertically. The right half is labeled \u201cIrrational Numbers\u201d. The left half is labeled \u201cRational Numbers\u201d and contains three concentric rectangles. The outer most rectangle is labeled \u201cIntegers\u201d, the next rectangle is \u201cWhole Numbers\u201d and the inner most rectangle is \u201cNatural Numbers\u201d.\" width=\"654\" height=\"396\" \/>\r\n<h3>The Order of Operations<\/h3>\r\n<ul>\r\n \t<li>Perform all operations within grouping symbols first. Grouping symbols include parentheses ( ), brackets [ ], braces { }, and fraction bars.<\/li>\r\n \t<li>Evaluate exponents or square roots.<\/li>\r\n \t<li>Multiply or divide, from left to right.<\/li>\r\n \t<li>Add or subtract, from left to right.<\/li>\r\n<\/ul>\r\nThis order of operations is true for all real numbers.\r\n<h2>Glossary:<\/h2>\r\n<dl id=\"fs-id1310436\" class=\"definition\">\r\n \t<dt><strong>Irrational number<\/strong><\/dt>\r\n \t<dd id=\"fs-id1166494771196\">A\u00a0number that cannot be written as the ratio of two integers. Its decimal form does not stop and does not repeat.<\/dd>\r\n<\/dl>\r\n<dl id=\"fs-id1166491228200\" class=\"definition\">\r\n \t<dt><strong>Rational number<\/strong><\/dt>\r\n \t<dd id=\"fs-id1166491428926\">A\u00a0number that can be written in the form [latex]{\\Large\\frac{p}{q}}[\/latex] , where <em>p<\/em> and <em>q<\/em> are integers and [latex]q\\ne 0[\/latex] . Its decimal form stops or repeats.<\/dd>\r\n<\/dl>\r\n<dl id=\"fs-id1712159\" class=\"definition\">\r\n \t<dt><strong>Real number:<\/strong><\/dt>\r\n \t<dd id=\"fs-id1166497278296\">A\u00a0number that is either rational or irrational.<\/dd>\r\n<\/dl>","rendered":"<h2>Key Concepts<\/h2>\n<ul id=\"eip-693\">\n<li><strong>Real numbers<\/strong><\/li>\n<\/ul>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24222311\/CNX_BMath_Figure_07_01_001.png\" alt=\"The image shows a large rectangle labeled \u201cReal Numbers\u201d. The rectangle is split in half vertically. The right half is labeled \u201cIrrational Numbers\u201d. The left half is labeled \u201cRational Numbers\u201d and contains three concentric rectangles. The outer most rectangle is labeled \u201cIntegers\u201d, the next rectangle is \u201cWhole Numbers\u201d and the inner most rectangle is \u201cNatural Numbers\u201d.\" width=\"654\" height=\"396\" \/><\/p>\n<h3>The Order of Operations<\/h3>\n<ul>\n<li>Perform all operations within grouping symbols first. Grouping symbols include parentheses ( ), brackets [ ], braces { }, and fraction bars.<\/li>\n<li>Evaluate exponents or square roots.<\/li>\n<li>Multiply or divide, from left to right.<\/li>\n<li>Add or subtract, from left to right.<\/li>\n<\/ul>\n<p>This order of operations is true for all real numbers.<\/p>\n<h2>Glossary:<\/h2>\n<dl id=\"fs-id1310436\" class=\"definition\">\n<dt><strong>Irrational number<\/strong><\/dt>\n<dd id=\"fs-id1166494771196\">A\u00a0number that cannot be written as the ratio of two integers. Its decimal form does not stop and does not repeat.<\/dd>\n<\/dl>\n<dl id=\"fs-id1166491228200\" class=\"definition\">\n<dt><strong>Rational number<\/strong><\/dt>\n<dd id=\"fs-id1166491428926\">A\u00a0number that can be written in the form [latex]{\\Large\\frac{p}{q}}[\/latex] , where <em>p<\/em> and <em>q<\/em> are integers and [latex]q\\ne 0[\/latex] . Its decimal form stops or repeats.<\/dd>\n<\/dl>\n<dl id=\"fs-id1712159\" class=\"definition\">\n<dt><strong>Real number:<\/strong><\/dt>\n<dd id=\"fs-id1166497278296\">A\u00a0number that is either rational or irrational.<\/dd>\n<\/dl>\n\n\t\t\t <section class=\"citations-section\" role=\"contentinfo\">\n\t\t\t <h3>Candela Citations<\/h3>\n\t\t\t\t\t <div>\n\t\t\t\t\t\t <div id=\"citation-list-9658\">\n\t\t\t\t\t\t\t <div class=\"licensing\"><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Specific attribution<\/div><ul class=\"citation-list\"><li>Prealgebra. <strong>Provided by<\/strong>: OpenStax. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em>. <strong>License Terms<\/strong>: Download for free at http:\/\/cnx.org\/contents\/caa57dab-41c7-455e-bd6f-f443cda5519c@9.757<\/li><\/ul><\/div>\n\t\t\t\t\t\t <\/div>\n\t\t\t\t\t <\/div>\n\t\t\t <\/section>","protected":false},"author":17533,"menu_order":7,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc-attribution\",\"description\":\"Prealgebra\",\"author\":\"\",\"organization\":\"OpenStax\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"Download for free at http:\/\/cnx.org\/contents\/caa57dab-41c7-455e-bd6f-f443cda5519c@9.757\"}]","CANDELA_OUTCOMES_GUID":"0c229a247d744e899bac14d9076cadaf","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-9658","chapter","type-chapter","status-publish","hentry"],"part":7349,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/wm-developmentalemporium\/wp-json\/pressbooks\/v2\/chapters\/9658","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/wm-developmentalemporium\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/wm-developmentalemporium\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/wm-developmentalemporium\/wp-json\/wp\/v2\/users\/17533"}],"version-history":[{"count":11,"href":"https:\/\/courses.lumenlearning.com\/wm-developmentalemporium\/wp-json\/pressbooks\/v2\/chapters\/9658\/revisions"}],"predecessor-version":[{"id":20431,"href":"https:\/\/courses.lumenlearning.com\/wm-developmentalemporium\/wp-json\/pressbooks\/v2\/chapters\/9658\/revisions\/20431"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/wm-developmentalemporium\/wp-json\/pressbooks\/v2\/parts\/7349"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/wm-developmentalemporium\/wp-json\/pressbooks\/v2\/chapters\/9658\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/wm-developmentalemporium\/wp-json\/wp\/v2\/media?parent=9658"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/wm-developmentalemporium\/wp-json\/pressbooks\/v2\/chapter-type?post=9658"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/wm-developmentalemporium\/wp-json\/wp\/v2\/contributor?post=9658"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/wm-developmentalemporium\/wp-json\/wp\/v2\/license?post=9658"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}