{"id":1475,"date":"2020-07-20T23:26:34","date_gmt":"2020-07-20T15:26:34","guid":{"rendered":"https:\/\/www.study-together.com\/edu\/?page_id=1475"},"modified":"2020-11-02T23:42:32","modified_gmt":"2020-11-02T15:42:32","slug":"rational-irrational-numbers","status":"publish","type":"page","link":"https:\/\/www.study-together.com\/edu\/secondary\/form3_maths\/rational-irrational-numbers\/","title":{"rendered":"4. \u6709\u7406\u6578\u53ca\u7121\u7406\u6578 (Rational &#038; Irrational Numbers)"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-page\" data-elementor-id=\"1475\" class=\"elementor elementor-1475\">\n\t\t\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-1f5feaa elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"1f5feaa\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-66 elementor-top-column elementor-element elementor-element-4b247ef\" data-id=\"4b247ef\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-efeec79 elementor-widget elementor-widget-text-editor\" data-id=\"efeec79\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<h2>4.1\u00a0 \u4ec0\u9ebc\u662f\u6709\u7406\u6578?\u4ec0\u9ebc\u662f\u7121\u7406\u6578?<\/h2><p>\u6709\u7406\u6578\u548c\u7121\u7406\u6578\u4e2d\u7684\u300c\u7406\u300d\uff0c\u5927\u5bb6\u53ef\u4ee5\u7406\u89e3\u70ba\u300c\u5408\u7406\u300d\u3001\u300c\u689d\u7406\u300d\u3001\u300c\u6709\u7406\u6027\u300d\u3002<\/p><p>\u5c0d\u6211\u4f86\u8aaa\uff0c\u4e00\u500b\u6578\u662f\u201c\u6709\u7406\u7684\u201d\u662f\u6307\u6211\u5011\u80fd<u>\u6e96\u78ba\u5730<\/u>\u638c\u63e1\u548c\u8868\u9054\u5230\u5b83\u7684\u503c\u662f\u591a\u5c11\u3002<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-7efd900 elementor-widget elementor-widget-text-editor\" data-id=\"7efd900\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<h2>4.1\u00a0 \u6709\u7406\u6578<\/h2><p>\u6240\u6709\u6574\u6578\u3001\u5206\u6578\u3001\u6709\u76e1\u5c0f\u6578\u548c\u5faa\u74b0\u5c0f\u6578\u90fd\u662f\u6709\u7406\u6578\u3002<\/p><p>\u5176\u5be6\u5927\u5bb6\u6309\u300c\u201c\u6709\u7406\u6578\u201d\u662f\u6307\u6211\u5011\u80fd<u>\u6e96\u78ba\u5730<\/u>\u638c\u63e1\u548c\u8868\u9054\u5b83\u7684\u503c\u7684\u6578\u300d\u5c31\u6703\u660e\u767d\u3002<\/p><ul><li style=\"list-style-type: none;\"><ul><li>\u6574\u6578\u7576\u7136\u53ef\u4ee5\u4e00\u500b\u500b\u5481\u6578\uff0c\u6240\u4ee5\u4fc2\u6709\u7406\u6578\u5514\u5947\u3002<\/li><li>\u00a0\u5206\u6578\u6211\u5730\u90fd\u53ef\u4ee5\u6e96\u78ba\u5730\u7406\u89e3\u5230\u4f62\u4fc2\u5e7e\u591a\u3002<ul><li>\u5c31\u7b97\u4fc2\\(dfrac{3}{23491}\\}\uff0c\u6211\u5730\u90fd\u77e5\u9053\u4fc2\u628a1\u5206\u621023491\u4efd\u5f8c\u76843\u4efd\u3002<\/li><\/ul><\/li><li>\u6709\u76e1\u5c0f\u6578\u56e0\u70ba\u53ef\u4ee5\u8b8a\u6210\u5206\u6578\uff0c\u6240\u4ee5\u90fd\u4fc2\u6709\u7406\u6578\u3002<ul><li>\u4f8b\u5982 \\(0.0023 = \\dfrac{23}{10000}\\)<\/li><\/ul><\/li><li>\u5faa\u74b0\u5c0f\u6578\u56e0\u70ba\u53ef\u4ee5\u8b8a\u6210\u923c\u6578\uff0c\u6240\u4ee5\u90fd\u4fc2\u6709\u7406\u6578\u3002<ul><li>\u4f8b\u5982 \\( 0.\\dot{1} = 0.111111111&#8230; = \\dfrac{1}{9}\\)<\/li><\/ul><\/li><\/ul><\/li><\/ul>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-aab7aa9 elementor-widget elementor-widget-text-editor\" data-id=\"aab7aa9\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<h2>4.2\u00a0 \u7121\u7406\u6578<\/h2><p>\u4e0d\u662f\u201c\u6709\u7406\u6578\u201d\u7684\u6578\u4fbf\u662f\u7121\u7406\u6578\u3002<\/p><p>\u6700\u5e38\u898b\u7684\u7121\u7406\u6578\u6709\u201c\u4e0d\u80fd\u5316\u7c21\u6210\u6574\u6578\u7684\u5e73\u65b9\u6839\u201d\uff08\u5982\\(\\sqrt{3}\\) \uff09\u548c\u00a0 \\(\\pi\\)\u3002<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-73fb932 elementor-widget elementor-widget-text-editor\" data-id=\"73fb932\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<h2>4.3\u00a0 \u6839\u5f0f\u7684\u904b\u7b97<\/h2><p>\u5927\u5bb6\u8981\u719f\u7fd2\u4ee5\u4e0b\u5e7e\u500b\u6700\u57fa\u672c\u7684\u6839\u5f0f\u904b\u7b97\uff0c<\/p><ul><li style=\"list-style-type: none;\"><ul><li>\\(\\sqrt{a} \\times \\sqrt{a} = a\\)<br \/>\u4f9d\u500b\u5176\u5be6\u4fc2\u6839\u5f0f\u7684\u5b9a\u7fa9\u3002<ul><li>\u4f8b1: \\(\\sqrt{5} \\times \\sqrt{5} = 5\\)<\/li><\/ul><\/li><li>\\(\\sqrt{a} + \\sqrt{a} = 2\\sqrt{a}\\)<ul><li>\u4f8b2: \\(\\sqrt{3} + \\sqrt{3} = 2\\sqrt{3}\\)<\/li><\/ul><\/li><li>\\(\\sqrt{a} \\times \\sqrt{b} = \\sqrt{ab}\\)<ul><li>\u4f8b3: \\(\\sqrt{3} \\times \\sqrt{5} = \\sqrt{15}\\)<\/li><\/ul><\/li><li>\\(\\dfrac{\\sqrt{a}}{\\sqrt{b}} = \\sqrt{\\dfrac{a}{b}}\\)<ul><li>\u4f8b4: \\(\\dfrac{\\sqrt{6}}{\\sqrt{3}} = \\sqrt{\\dfrac{6}{3}} = \\sqrt{2} \\)<\/li><\/ul><\/li><\/ul><\/li><\/ul>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-f11fd88 elementor-widget elementor-widget-text-editor\" data-id=\"f11fd88\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<h2>4.4\u00a0 \u6839\u5f0f\u7684\u5316\u7c21<\/h2><p>\u5316\u7c21\u4e00\u500b\u6839\u5f0f\u662f\u6307\u628a\u6839\u865f\u5167\u7684\u6578\u5316\u6210\u6700\u5c0f\u7684\u6574\u6578\u3002\u9019\u6709\u9ede\u50cf\u6211\u5011\u5316\u7c21\u5206\u6578\u6642\u628a\u5206\u6bcd\u548c\u5206\u5b50\u201c\u76f8\u7d04\u201d\u6210\u6700\u5c0f\u7684\u6574\u6578\u3002<\/p><p>\u4f8b5\uff1a \u5316\u7c21 \\(\\sqrt{12}\\)<br \/>\u89e3\uff1a\u3000\\(\\sqrt{12} = \\sqrt{2 \\times 2 \\times 3} = 2\\sqrt{3}\\)<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-21cd38f elementor-widget elementor-widget-text-editor\" data-id=\"21cd38f\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<h2>4.5\u00a0 \u6709\u7406\u5316<\/h2><p>\u628a\u4e00\u500b\u5206\u6bcd\u662f\u7121\u7406\u6578\u7684\u5206\u6578\u201c\u6709\u7406\u5316\u201d\u5c31\u662f\u628a\u5206\u6bcd\u7684\u7121\u7406\u6578\u5316\u6210\u6709\u7406\u6578\u7684\u904e\u7a0b\u3002<\/p><p>\u4f8b\u5b50\uff1a\u00a0\u00a0 \u6709\u7406\u5316\\(\\dfrac{2}{\\sqrt{3}}\\)<br \/>\u89e3\uff1a\\(\\quad \\dfrac{2}{\\sqrt{3}} = \\dfrac{2}{\\sqrt{3}}\u00a0 \\times \\dfrac{\\sqrt{3}}{\\sqrt{3}} = \\dfrac{2\\sqrt{3}}{3}\\)<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<section class=\"elementor-section elementor-inner-section elementor-element elementor-element-4b1204e elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"4b1204e\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-757fab4\" data-id=\"757fab4\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-44f7eca elementor-widget elementor-widget-text-editor\" data-id=\"44f7eca\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<a href=\"https:\/\/www.study-together.com\/edu\/secondary\/form3_maths\/use-of-percentage\/\"><i class=\"far fa-arrow-alt-circle-left\" aria-hidden=\"true\"><\/i> \u767e\u5206\u6cd5<\/a>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-0ed2eb5\" data-id=\"0ed2eb5\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-189b176\" data-id=\"189b176\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-b81d549 elementor-widget elementor-widget-text-editor\" data-id=\"b81d549\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p style=\"text-align: right;\"><a href=\"https:\/\/www.study-together.com\/edu\/secondary\/form3_maths\/deductive-geometry\/\">\u6f14\u7e79\u5e7e\u4f55 <i class=\"far fa-arrow-alt-circle-right\" aria-hidden=\"true\"><\/i><\/a><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-0c96e6f\" data-id=\"0c96e6f\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-db503d9 elementor-widget elementor-widget-sidebar\" data-id=\"db503d9\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"sidebar.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"sidebar-box widget-oceanwp-custom-menu custom-menu-widget clr\"><style type=\"text\/css\">.ocean_custom_menu-4 > ul > li > a, .custom-menu-widget .ocean_custom_menu-4 .dropdown-menu .sub-menu li a.menu-link{font-size:16px;line-height:17px;}.custom-menu-widget .ocean_custom_menu-4.oceanwp-custom-menu > ul.click-menu .open-this{font-size:16px;}<\/style><h4 class=\"widget-title\">\u4e2d\u4e09\u6578\u5b78\u3010\u76ee\u9304\u3011<\/h4><div class=\"oceanwp-custom-menu clr ocean_custom_menu-4 left dropdown-hover\"><ul id=\"menu-form3mathstopics\" class=\"dropdown-menu sf-menu\"><li  id=\"menu-item-1543\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-1543\"><a href=\"https:\/\/www.study-together.com\/edu\/secondary\/form3_maths\/inequalities\/\" class=\"menu-link\">1. \u4e0d\u7b49\u5f0f (Inequalities)<\/a><\/li>\n<li  id=\"menu-item-1542\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-1542\"><a href=\"https:\/\/www.study-together.com\/edu\/secondary\/form3_maths\/indices\/\" class=\"menu-link\">2. \u6307\u6578 (Indices)<\/a><\/li>\n<li  id=\"menu-item-1541\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-1541\"><a href=\"https:\/\/www.study-together.com\/edu\/secondary\/form3_maths\/use-of-percentage\/\" class=\"menu-link\">3. \u767e\u4efd\u6cd5  (Use of Percentage)<\/a><\/li>\n<li  id=\"menu-item-1540\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-1540\"><a href=\"https:\/\/www.study-together.com\/edu\/secondary\/form3_maths\/rational-irrational-numbers\/\" class=\"menu-link\">4. \u6709\u7406\u6578\u53ca\u7121\u7406\u6578 (Rational &#038; Irrational Numbers)<\/a><\/li>\n<li  id=\"menu-item-1539\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-1539\"><a href=\"https:\/\/www.study-together.com\/edu\/secondary\/form3_maths\/deductive-geometry\/\" class=\"menu-link\">5. \u6f14\u7e79\u5e7e\u4f55 (Deductive Geometry)<\/a><\/li>\n<li  id=\"menu-item-1538\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-1538\"><a href=\"https:\/\/www.study-together.com\/edu\/secondary\/form3_maths\/quadrilateral\/\" class=\"menu-link\">6. \u56db\u908a\u5f62 (Quadrilateral)<\/a><\/li>\n<li  id=\"menu-item-1537\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-1537\"><a href=\"https:\/\/www.study-together.com\/edu\/secondary\/form3_maths\/area-volume\/\" class=\"menu-link\">7. \u9762\u7a4d\u8207\u9ad4\u7a4d (Area &#038; Volume)<\/a><\/li>\n<li  id=\"menu-item-1536\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-1536\"><a href=\"https:\/\/www.study-together.com\/edu\/secondary\/form3_maths\/coordinate-geometry\/\" class=\"menu-link\">8. \u5750\u6a19\u5e7e\u4f55 (Coordinate Geometry)<\/a><\/li>\n<li  id=\"menu-item-1535\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-1535\"><a href=\"https:\/\/www.study-together.com\/edu\/secondary\/form3_maths\/trigonometry\/\" class=\"menu-link\">9. \u4e09\u89d2\u5b78 (Trigonometry)<\/a><\/li>\n<li  id=\"menu-item-1534\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-1534\"><a href=\"https:\/\/www.study-together.com\/edu\/secondary\/form3_maths\/applications-of-trigonometry\/\" class=\"menu-link\">10. \u4e09\u89d2\u6bd4\u7684\u61c9\u7528 (Applications of Trigonometry)<\/a><\/li>\n<li  id=\"menu-item-1533\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-1533\"><a href=\"https:\/\/www.study-together.com\/edu\/secondary\/form3_maths\/probability\/\" class=\"menu-link\">11. \u6982\u7387 (Probability)<\/a><\/li>\n<li  id=\"menu-item-1532\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-1532\"><a href=\"https:\/\/www.study-together.com\/edu\/secondary\/form3_maths\/statistics-measure-of-central-tendency\/\" class=\"menu-link\">12. \u7d71\u8a08 \u2013 \u96c6\u4e2d\u8da8\u52e2\u7684\u91cf\u5ea6 (Measure of Central Tendency)<\/a><\/li>\n<li  id=\"menu-item-1625\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-1625\"><a href=\"https:\/\/www.study-together.com\/edu\/secondary\/form3_maths\/centers-of-triangles\/\" class=\"menu-link\">13. \u4e09\u89d2\u5f62\u7684\u5fc3 (Centers of Triangles)<\/a><\/li>\n<li  id=\"menu-item-16136\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-16136\"><a href=\"https:\/\/www.study-together.com\/edu\/secondary\/exam_papers\/\" class=\"menu-link\">*** \u521d\u4e2d\u8a66\u5377 \/ \u8a66\u984c\u5eab ***<\/a><\/li>\n<\/ul><\/div><\/div>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"<p>4.1\u00a0 \u4ec0\u9ebc\u662f\u6709\u7406\u6578?\u4ec0\u9ebc\u662f\u7121\u7406\u6578? \u6709\u7406\u6578\u548c\u7121\u7406\u6578\u4e2d\u7684\u300c\u7406\u300d\uff0c\u5927\u5bb6\u53ef\u4ee5\u7406\u89e3\u70ba\u300c\u5408\u7406\u300d\u3001\u300c\u689d\u7406\u300d\u3001\u300c\u6709\u7406\u6027\u300d 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