{"id":15,"date":"2022-04-13T09:44:28","date_gmt":"2022-04-13T09:44:28","guid":{"rendered":"http:\/\/10thclass.deltapublications.in\/?page_id=15"},"modified":"2025-07-31T11:07:42","modified_gmt":"2025-07-31T11:07:42","slug":"a-3-identify-rational-and-irrational-numbers","status":"publish","type":"page","link":"https:\/\/10thclass.deltapublications.in\/index.php\/a-3-identify-rational-and-irrational-numbers\/","title":{"rendered":"A.3 Identify rational and irrational numbers"},"content":{"rendered":"\n<h3 class=\"wp-block-heading has-text-align-center has-text-color has-huge-font-size\" style=\"color:#00056d;text-transform:uppercase\"><strong>Identify rational and irrational numbers<\/strong><\/h3>\n\n\n\n<figure class=\"wp-block-video\"><video controls src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/07\/A.3-Identify-rational-and-irrational-numbers.mp4\"><\/video><\/figure>\n\n\n\n<p class=\"has-text-color has-link-color has-large-font-size wp-elements-7d74d42bd3679a207fd6036ccd5c9fa3\" style=\"color:#74008b;text-transform:uppercase\">Key notes :<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-text-color has-link-color has-fixed-layout\" style=\"color:#000060\"><tbody><tr><td><strong>Definitions:<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p class=\"has-normal-font-size\"><strong>Rational Numbers:<\/strong> Numbers that can be expressed as a fraction of two integers (a\/b), where b is not zero.<\/p>\n\n\n\n<p class=\"has-normal-font-size\"><strong>Irrational Numbers:<\/strong> Numbers that cannot be expressed as a fraction of two integers and have non-terminating, non-repeating decimal expansions.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity is-style-wide\"\/>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-text-color has-link-color has-fixed-layout\" style=\"color:#000060\"><tbody><tr><td><strong>Examples:<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p class=\"has-normal-font-size\"><strong>Rational Numbers: <\/strong>2, -5, 3\/4, -1.25, \u221a9 (which is 3), etc.<\/p>\n\n\n\n<p class=\"has-normal-font-size\"><strong>Irrational Numbers:<\/strong> \u221a2, \u03c0 (pi), \u221a5, e (Euler&#8217;s number), 2.15264123&#8230;&#8230; etc.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity is-style-wide\"\/>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-text-color has-link-color has-fixed-layout\" style=\"color:#000060\"><tbody><tr><td><strong>Characteristics:<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p class=\"has-normal-font-size\">Rational numbers either terminate or repeat in their decimal form.<\/p>\n\n\n\n<p class=\"has-normal-font-size\">Irrational numbers have decimal expansions that neither terminate nor repeat.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity is-style-wide\"\/>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-text-color has-link-color has-fixed-layout\" style=\"color:#000060\"><tbody><tr><td><strong>Characteristics:<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p class=\"has-normal-font-size\"><strong>Decimal Form:<\/strong> Convert the number to decimal form. If it terminates or repeats, it&#8217;s rational; if not, it&#8217;s irrational.<\/p>\n\n\n\n<p class=\"has-normal-font-size\"><strong>Square Root Test:<\/strong> If a number&#8217;s square root is not a perfect square, it&#8217;s irrational.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity is-style-wide\"\/>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-text-color has-link-color has-fixed-layout\" style=\"color:#000060\"><tbody><tr><td><strong><strong>Closure Properties:<\/strong><\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p class=\"has-normal-font-size\">Rational numbers are closed under addition, subtraction, multiplication, and division (except division by zero).<\/p>\n\n\n\n<p class=\"has-normal-font-size\">Adding or multiplying a rational number with an irrational number results in an irrational number.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity is-style-wide\"\/>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-text-color has-link-color has-fixed-layout\" style=\"color:#000060\"><tbody><tr><td><strong>Importance:<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p class=\"has-normal-font-size\">Understanding rational and irrational numbers helps in calculations involving precise measurements and theoretical concepts in mathematics and sciences.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity is-style-dots\"\/>\n\n\n\n<p class=\"has-text-align-center has-text-color has-normal-font-size\" style=\"color:#105000\"><strong>Learn with an example<\/strong><\/p>\n\n\n\n<div class=\"wp-block-group has-background has-normal-font-size\" style=\"background-color:#e391fb\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<div class=\"wp-block-group has-background-background-color has-background\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<p class=\"has-text-color has-link-color wp-elements-a165df85cdb9ab06e9b29457dc7bf261\" style=\"color:#b00012\">is 2\/10 an irrational number?<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>yes<\/li>\n\n\n\n<li>no<\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n<p>2\/10 is a fraction.&nbsp;So, 2\/10 is not an irrational number.<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-normal-font-size\" style=\"background-color:#a78af7\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<div class=\"wp-block-group has-background-background-color has-background\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<p class=\"has-text-color has-link-color wp-elements-09aad348889a519579245653f56133ef\" style=\"color:#b00012\">Which of the following describes \u221a2?<\/p>\n\n\n\n<p> Select all that apply.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>irrational number <\/li>\n\n\n\n<li>rational number<\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n<p>\u221a2 (which is 1.41421\u2026) cannot be written as a fraction, a terminating decimal, or a repeating decimal. So, \u221a2 is not a rational number.<\/p>\n\n\n\n<p>Since \u221a2 is not a rational number, it is an irrational number.<\/p>\n\n\n\n<p>There is one correct answer choice. \u221a2 is an irrational number.<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-normal-font-size\" style=\"background-color:#88f3ea\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<div class=\"wp-block-group has-background-background-color has-background\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<p class=\"has-text-color has-link-color wp-elements-f94de72b86a8e92b06287381631a0ec2\" style=\"color:#b00012\">Which of the following describes 5\/6? <\/p>\n\n\n\n<p>Select all that apply.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>irrational number <\/li>\n\n\n\n<li>rational number<\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n<p>5\/6 is a fraction.&nbsp;So, 5\/6 (which is 5\/6 ) is a rational number.<\/p>\n\n\n\n<p>Since 5\/6 is a rational number, it is not an irrational number.<\/p>\n\n\n\n<p>There is one correct answer choice. 5\/6 is a rational number.<\/p>\n<\/div><\/div>\n\n\n\n<p class=\"has-text-color has-large-font-size\" style=\"color:#d90000\">Let&#8217;s Practice!<\/p>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-full\"><a href=\"https:\/\/wordwall.net\/play\/95402\/670\/851\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-1.png\" alt=\"\" class=\"wp-image-6368\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-1.png 500w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-1-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-1-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-full\"><a href=\"https:\/\/wordwall.net\/play\/34609\/989\/697\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-1.png\" alt=\"\" class=\"wp-image-6369\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-1.png 500w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-1-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-1-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Identify rational and irrational numbers Key notes : Definitions: Rational Numbers: Numbers that can be expressed as a fraction of two integers (a\/b), where b is not zero. Irrational Numbers: Numbers that cannot be expressed as a fraction of two integers and have non-terminating, non-repeating decimal expansions. Examples: Rational Numbers: 2, -5, 3\/4, -1.25, \u221a9<a class=\"more-link\" href=\"https:\/\/10thclass.deltapublications.in\/index.php\/a-3-identify-rational-and-irrational-numbers\/\">Continue reading <span class=\"screen-reader-text\">&#8220;A.3 Identify rational and irrational numbers&#8221;<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"om_disable_all_campaigns":false,"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"footnotes":""},"class_list":["post-15","page","type-page","status-publish","hentry","entry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/15","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/comments?post=15"}],"version-history":[{"count":27,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/15\/revisions"}],"predecessor-version":[{"id":18180,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/15\/revisions\/18180"}],"wp:attachment":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=15"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}