{"id":15987,"date":"2021-04-01T23:47:50","date_gmt":"2021-04-01T23:47:50","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/nwfsc-MGF1107\/chapter\/introduction-classifying-real-numbers\/"},"modified":"2021-06-30T14:05:44","modified_gmt":"2021-06-30T14:05:44","slug":"introduction-classifying-real-numbers","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/nwfsc-MGF1107\/chapter\/introduction-classifying-real-numbers\/","title":{"raw":"Introduction to Classes of Real Numbers","rendered":"Introduction to Classes of Real Numbers"},"content":{"raw":"<h2>What you'll learn to do: Classify real numbers as counting, whole, rational, irrational, or integers<\/h2>\r\n[caption id=\"\" align=\"aligncenter\" width=\"716\"]<img class=\"\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24222308\/CNX_BMath_Figure_07_00_001.png\" alt=\"A colorful quilt \" width=\"716\" height=\"330\" \/> A patchwork quilt combines many colorful pieces of fabric into an interesting pattern.[\/caption]\r\n\r\nQuiltmakers know that by rearranging the same basic blocks the resulting quilts can look very different. What happens when we rearrange the numbers in an expression? Does the resulting value change? We will answer these questions in this chapter as we will learn about the properties of numbers.\r\n\r\nA quilt is formed by sewing many different pieces of fabric together. The pieces can vary in color, size, and shape. The combinations of different kinds of pieces provide for an endless possibility of patterns. Much like the pieces of fabric, mathematicians distinguish among different types of numbers. The kinds of numbers in an expression provide for an endless possibility of outcomes. In this chapter, we will learn about different types of numbers and their properties.\r\n\r\nBefore you get started in this module, try a few practice problems and review\u00a0prior\u00a0concepts.\r\n<div class=\"textbox examples\">\r\n<h3>readiness quiz<\/h3>\r\n1)[ohm_question]148235[\/ohm_question]\r\n\r\n&nbsp;\r\n\r\n2)[ohm_question]146253[\/ohm_question]\r\n\r\nIf you missed this problem, review the video below.\r\n\r\nhttps:\/\/youtu.be\/P0IB7LfeaU4\r\n\r\n3)[ohm_question]146618[\/ohm_question]\r\n\r\nIf you missed this problem, review this video.\r\n\r\nhttps:\/\/youtu.be\/rDpIm_EepcE\r\n\r\n<\/div>","rendered":"<h2>What you&#8217;ll learn to do: Classify real numbers as counting, whole, rational, irrational, or integers<\/h2>\n<div style=\"width: 726px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" class=\"\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24222308\/CNX_BMath_Figure_07_00_001.png\" alt=\"A colorful quilt\" width=\"716\" height=\"330\" \/><\/p>\n<p class=\"wp-caption-text\">A patchwork quilt combines many colorful pieces of fabric into an interesting pattern.<\/p>\n<\/div>\n<p>Quiltmakers know that by rearranging the same basic blocks the resulting quilts can look very different. What happens when we rearrange the numbers in an expression? Does the resulting value change? We will answer these questions in this chapter as we will learn about the properties of numbers.<\/p>\n<p>A quilt is formed by sewing many different pieces of fabric together. The pieces can vary in color, size, and shape. The combinations of different kinds of pieces provide for an endless possibility of patterns. Much like the pieces of fabric, mathematicians distinguish among different types of numbers. The kinds of numbers in an expression provide for an endless possibility of outcomes. In this chapter, we will learn about different types of numbers and their properties.<\/p>\n<p>Before you get started in this module, try a few practice problems and review\u00a0prior\u00a0concepts.<\/p>\n<div class=\"textbox examples\">\n<h3>readiness quiz<\/h3>\n<p>1)<iframe loading=\"lazy\" id=\"ohm148235\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=148235&theme=oea&iframe_resize_id=ohm148235&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<p>&nbsp;<\/p>\n<p>2)<iframe loading=\"lazy\" id=\"ohm146253\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146253&theme=oea&iframe_resize_id=ohm146253&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<p>If you missed this problem, review the video below.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-1\" title=\"Ex 1:  Convert a Fraction to a Decimal (terminating)\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/P0IB7LfeaU4?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<p>3)<iframe loading=\"lazy\" id=\"ohm146618\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146618&theme=oea&iframe_resize_id=ohm146618&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<p>If you missed this problem, review this video.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-2\" title=\"Simplify Square Roots (Perfect Squares)\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/rDpIm_EepcE?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<\/div>\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-15987\">\n\t\t\t\t\t\t\t <div class=\"licensing\"><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Shared previously<\/div><ul class=\"citation-list\"><li>Ex 1: Convert a Fraction to a Decimal (terminating). <strong>Authored by<\/strong>: James Sousa (Mathispower4u.com). <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/P0IB7LfeaU4\">https:\/\/youtu.be\/P0IB7LfeaU4<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><li>Simplify Square Roots (Perfect Squares). <strong>Authored by<\/strong>: James Sousa (Mathispower4u.com) . <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/rDpIm_EepcE\">https:\/\/youtu.be\/rDpIm_EepcE<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><li>Question ID: 146253, 146618. <strong>Authored by<\/strong>: Lumen Learning. <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>: IMathAS Community License CC-BY + GPL<\/li><\/ul><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 class=\"license-attribution-dropdown-subheading\">Public domain content<\/div><ul class=\"citation-list\"><li>Patchwork quilt. <strong>Authored by<\/strong>: Hans. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/pixabay.com\/en\/patchwork-quilt-patchwork-100158\/\">https:\/\/pixabay.com\/en\/patchwork-quilt-patchwork-100158\/<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/about\/pdm\">Public Domain: No Known Copyright<\/a><\/em><\/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":167848,"menu_order":2,"template":"","meta":{"_candela_citation":"[{\"type\":\"pd\",\"description\":\"Patchwork quilt\",\"author\":\"Hans\",\"organization\":\"\",\"url\":\"https:\/\/pixabay.com\/en\/patchwork-quilt-patchwork-100158\/\",\"project\":\"\",\"license\":\"pd\",\"license_terms\":\"\"},{\"type\":\"cc-attribution\",\"description\":\"Prealgebra\",\"author\":\"\",\"organization\":\"OpenStax\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"Download for free at 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