{"id":1877,"date":"2023-11-22T20:16:40","date_gmt":"2023-11-22T19:16:40","guid":{"rendered":"http:\/\/localhost:8080\/maxblog\/?p=1877"},"modified":"2023-11-22T23:48:46","modified_gmt":"2023-11-22T22:48:46","slug":"manipuler-les-nombres-reels","status":"publish","type":"post","link":"https:\/\/www.maxdecours.com\/maxblog\/manipuler-les-nombres-reels\/","title":{"rendered":"Manipuler les nombres r\u00e9els"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-post\" data-elementor-id=\"1877\" class=\"elementor elementor-1877\">\n\t\t\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-7d71a4a elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"7d71a4a\" data-element_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-100 elementor-top-column elementor-element elementor-element-389cd7d\" data-id=\"389cd7d\" data-element_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-a8169f1 elementor-widget elementor-widget-spacer\" data-id=\"a8169f1\" data-element_type=\"widget\" data-widget_type=\"spacer.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-spacer\">\n\t\t\t<div class=\"elementor-spacer-inner\"><\/div>\n\t\t<\/div>\n\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<section class=\"elementor-section elementor-top-section elementor-element elementor-element-7643655 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"7643655\" data-element_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-100 elementor-top-column elementor-element elementor-element-f297427\" data-id=\"f297427\" data-element_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-361d80f elementor-widget elementor-widget-heading\" data-id=\"361d80f\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-heading-title elementor-size-xl\">Manipuler les nombres r\u00e9els<\/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<section class=\"elementor-section elementor-top-section elementor-element elementor-element-c2bda19 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"c2bda19\" data-element_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-100 elementor-top-column elementor-element elementor-element-d178bc4\" data-id=\"d178bc4\" data-element_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\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-de06178 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"de06178\" data-element_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-100 elementor-top-column elementor-element elementor-element-cc24190\" data-id=\"cc24190\" data-element_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\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-b7c611b elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"b7c611b\" data-element_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-100 elementor-top-column elementor-element elementor-element-9a7e2c2\" data-id=\"9a7e2c2\" data-element_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-fffe349 nc-justify-text elementor-widget elementor-widget-text-editor\" data-id=\"fffe349\" data-element_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<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_82_2 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\" style=\"cursor:inherit\">Table of Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" aria-label=\"Toggle Table of Content\"><span class=\"ez-toc-js-icon-con\"><span class=\"\"><span class=\"eztoc-hide\" style=\"display:none;\">Toggle<\/span><span class=\"ez-toc-icon-toggle-span\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/span><\/span><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1 ' ><li class='ez-toc-page-1 ez-toc-heading-level-1'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/www.maxdecours.com\/maxblog\/manipuler-les-nombres-reels\/#Introduction\" >Introduction<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-1'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/www.maxdecours.com\/maxblog\/manipuler-les-nombres-reels\/#Cours\" >Cours<\/a><ul class='ez-toc-list-level-2' ><li class='ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/www.maxdecours.com\/maxblog\/manipuler-les-nombres-reels\/#1_Ensemble_%E2%84%9D_des_nombres_reels_droite_numerique\" >1. Ensemble \u211d des nombres r\u00e9els, droite num\u00e9rique :<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/www.maxdecours.com\/maxblog\/manipuler-les-nombres-reels\/#2_Intervalles_de_%E2%84%9D_Notations_%E2%88%9E_et_-%E2%88%9E\" >2. Intervalles de \u211d. Notations +\u221e et -\u221e :<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/www.maxdecours.com\/maxblog\/manipuler-les-nombres-reels\/#3_Notation_a_Distance_entre_deux_nombres_reels\" >3. Notation |a|. Distance entre deux nombres r\u00e9els :<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/www.maxdecours.com\/maxblog\/manipuler-les-nombres-reels\/#4_Representation_de_lintervalle_a_%E2%80%93_r_a_r_et_caracterisation_par_la_condition_x_%E2%80%93_a_%E2%A9%BD_r\" >4. Repr\u00e9sentation de l&rsquo;intervalle [a &#8211; r, a + r] et caract\u00e9risation par la\ncondition |x &#8211; a| \u2a7d r :<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/www.maxdecours.com\/maxblog\/manipuler-les-nombres-reels\/#5_Ensemble_%F0%9D%94%BB_des_nombres_decimaux_Encadrement_decimal_dun_nombre_reel_a_10_puissance_-n_pres\" >5. Ensemble \ud835\udd3b des nombres d\u00e9cimaux. Encadrement\nd\u00e9cimal d&rsquo;un nombre r\u00e9el \u00e0 10 puissance -n pr\u00e8s :<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/www.maxdecours.com\/maxblog\/manipuler-les-nombres-reels\/#6_Ensemble_%E2%84%9A_des_nombres_rationnels_Nombres_irrationnels\" >6. Ensemble \u211a des nombres rationnels. Nombres irrationnels :<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-1'><a class=\"ez-toc-link ez-toc-heading-9\" href=\"https:\/\/www.maxdecours.com\/maxblog\/manipuler-les-nombres-reels\/#Methodes\" >M\u00e9thodes :<\/a><ul class='ez-toc-list-level-2' ><li class='ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-10\" href=\"https:\/\/www.maxdecours.com\/maxblog\/manipuler-les-nombres-reels\/#1_Associer_a_chaque_point_de_la_droite_graduee_un_unique_nombre_reel_et_reciproquement\" >1. Associer \u00e0 chaque point de la droite gradu\u00e9e un unique nombre r\u00e9el et r\u00e9ciproquement\n:<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-11\" href=\"https:\/\/www.maxdecours.com\/maxblog\/manipuler-les-nombres-reels\/#2_Representer_un_intervalle_de_la_droite_numerique_et_determiner_si_un_nombre_reel_appartient_a_un_intervalle_donne\" >2. Repr\u00e9senter un intervalle de la droite num\u00e9rique et d\u00e9terminer si un\nnombre r\u00e9el appartient \u00e0 un intervalle donn\u00e9 :<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-12\" href=\"https:\/\/www.maxdecours.com\/maxblog\/manipuler-les-nombres-reels\/#3_Donner_un_encadrement_damplitude_donnee_dun_nombre_reel_par_des_decimaux\" >3. Donner un encadrement, d&rsquo;amplitude donn\u00e9e, d\u2019un nombre r\u00e9el par des\nd\u00e9cimaux :<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-13\" href=\"https:\/\/www.maxdecours.com\/maxblog\/manipuler-les-nombres-reels\/#4_Arrondir_en_donnant_le_nombre_de_chiffres_significatifs_adapte_a_la_situation_etudiee\" >4. Arrondir en donnant le nombre de chiffres significatifs adapt\u00e9 \u00e0 la\nsituation \u00e9tudi\u00e9e :<\/a><\/li><\/ul><\/li><\/ul><\/nav><\/div>\n<h1><span class=\"ez-toc-section\" id=\"Introduction\"><\/span>Introduction<span class=\"ez-toc-section-end\"><\/span><\/h1>\n\n<p class=\"MsoNormal\"><span style=\"mso-fareast-font-family:&quot;Times New Roman&quot;;\nmso-bidi-font-family:Calibri;mso-bidi-theme-font:minor-latin;mso-fareast-language:\nFR\">&nbsp;<\/span><\/p>\n\n<p class=\"MsoNormal\"><span style=\"mso-fareast-font-family:&quot;Times New Roman&quot;;\nmso-bidi-font-family:Calibri;mso-bidi-theme-font:minor-latin;mso-fareast-language:\nFR\">La manipulation des nombres r\u00e9els est essentielle dans divers domaines des\nmath\u00e9matiques et de la science. Comprendre les caract\u00e9ristiques des diff\u00e9rents\nsous-ensembles de <\/span><span style=\"font-family:&quot;Cambria Math&quot;,serif;\nmso-fareast-font-family:&quot;Times New Roman&quot;;mso-bidi-font-family:&quot;Cambria Math&quot;;\nmso-fareast-language:FR\">\u211d<\/span><span style=\"mso-fareast-font-family:&quot;Times New Roman&quot;;\nmso-bidi-font-family:Calibri;mso-bidi-theme-font:minor-latin;mso-fareast-language:\nFR\">, tels que <\/span><span style=\"font-family:&quot;Cambria Math&quot;,serif;mso-fareast-font-family:\n&quot;Times New Roman&quot;;mso-bidi-font-family:&quot;Cambria Math&quot;;mso-fareast-language:\nFR\">\u211a<\/span><span style=\"mso-fareast-font-family:&quot;Times New Roman&quot;;mso-bidi-font-family:\nCalibri;mso-bidi-theme-font:minor-latin;mso-fareast-language:FR\">, <\/span><span style=\"font-family:&quot;Cambria Math&quot;,serif;mso-fareast-font-family:&quot;Times New Roman&quot;;\nmso-bidi-font-family:&quot;Cambria Math&quot;;mso-fareast-language:FR\">\ud835\udd3b<\/span><span style=\"mso-fareast-font-family:&quot;Times New Roman&quot;;mso-bidi-font-family:Calibri;\nmso-bidi-theme-font:minor-latin;mso-fareast-language:FR\">, et les nombres\nirrationnels, ainsi que les notions d&rsquo;intervalle et de distance, est crucial\npour travailler efficacement avec les nombres r\u00e9els.<\/span><\/p>\n\n<p class=\"MsoNormal\"><span style=\"mso-fareast-font-family:&quot;Times New Roman&quot;;\nmso-bidi-font-family:Calibri;mso-bidi-theme-font:minor-latin;mso-fareast-language:\nFR\">&nbsp;<\/span><\/p>\n\n<h1><span class=\"ez-toc-section\" id=\"Cours\"><\/span><span style=\"mso-fareast-font-family:&quot;Times New Roman&quot;;mso-fareast-language:\nFR\">Cours<\/span><span class=\"ez-toc-section-end\"><\/span><\/h1>\n\n<p class=\"MsoNormal\"><span style=\"mso-fareast-font-family:&quot;Times New Roman&quot;;\nmso-bidi-font-family:Calibri;mso-bidi-theme-font:minor-latin;mso-fareast-language:\nFR\">&nbsp;<\/span><\/p>\n\n<h2><span class=\"ez-toc-section\" id=\"1_Ensemble_%E2%84%9D_des_nombres_reels_droite_numerique\"><\/span><span style=\"mso-fareast-font-family:&quot;Times New Roman&quot;;mso-fareast-language:\nFR\">1. Ensemble <\/span><span style=\"font-family:&quot;Cambria Math&quot;,serif;\nmso-fareast-font-family:&quot;Times New Roman&quot;;mso-bidi-font-family:&quot;Cambria Math&quot;;\nmso-fareast-language:FR\">\u211d<\/span><span style=\"mso-fareast-font-family:&quot;Times New Roman&quot;;\nmso-fareast-language:FR\"> des nombres r\u00e9els, droite num\u00e9rique :<\/span><span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n<p class=\"MsoNormal\"><span style=\"mso-fareast-font-family:&quot;Times New Roman&quot;;\nmso-bidi-font-family:Calibri;mso-bidi-theme-font:minor-latin;mso-fareast-language:\nFR\">&nbsp;<\/span><\/p>\n\n<p class=\"MsoNormal\"><span style=\"mso-fareast-font-family:&quot;Times New Roman&quot;;\nmso-bidi-font-family:Calibri;mso-bidi-theme-font:minor-latin;mso-fareast-language:\nFR\">L&rsquo;ensemble des nombres r\u00e9els, not\u00e9 <\/span><span style=\"font-family:&quot;Cambria Math&quot;,serif;\nmso-fareast-font-family:&quot;Times New Roman&quot;;mso-bidi-font-family:&quot;Cambria Math&quot;;\nmso-fareast-language:FR\">\u211d<\/span><span style=\"mso-fareast-font-family:&quot;Times New Roman&quot;;\nmso-bidi-font-family:Calibri;mso-bidi-theme-font:minor-latin;mso-fareast-language:\nFR\">, est constitu\u00e9 de l&rsquo;ensemble des nombres qui peuvent \u00eatre repr\u00e9sent\u00e9s sur\nune droite num\u00e9rique. Cette droite s&rsquo;\u00e9tend \u00e0 l&rsquo;infini dans les deux directions\net chaque point sur cette droite correspond \u00e0 un nombre r\u00e9el unique. Les\nnombres r\u00e9els comprennent \u00e0 la fois les nombres rationnels (qui peuvent \u00eatre\nexprim\u00e9s comme le quotient de deux entiers) et les nombres irrationnels (qui ne\npeuvent pas \u00eatre exprim\u00e9s de cette mani\u00e8re).<\/span><\/p>\n\n<p class=\"MsoNormal\"><span style=\"mso-fareast-font-family:&quot;Times New Roman&quot;;\nmso-bidi-font-family:Calibri;mso-bidi-theme-font:minor-latin;mso-fareast-language:\nFR\">&nbsp;<\/span><\/p>\n\n<h2><span class=\"ez-toc-section\" id=\"2_Intervalles_de_%E2%84%9D_Notations_%E2%88%9E_et_-%E2%88%9E\"><\/span><span style=\"mso-fareast-font-family:&quot;Times New Roman&quot;;mso-fareast-language:\nFR\">2. Intervalles de <\/span><span style=\"font-family:&quot;Cambria Math&quot;,serif;\nmso-fareast-font-family:&quot;Times New Roman&quot;;mso-bidi-font-family:&quot;Cambria Math&quot;;\nmso-fareast-language:FR\">\u211d<\/span><span style=\"mso-fareast-font-family:&quot;Times New Roman&quot;;\nmso-fareast-language:FR\">. Notations +\u221e et -\u221e :<\/span><span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n<p class=\"MsoNormal\"><span style=\"mso-fareast-font-family:&quot;Times New Roman&quot;;\nmso-bidi-font-family:Calibri;mso-bidi-theme-font:minor-latin;mso-fareast-language:\nFR\">&nbsp;<\/span><\/p>\n\n<p class=\"MsoNormal\"><span style=\"mso-fareast-font-family:&quot;Times New Roman&quot;;\nmso-bidi-font-family:Calibri;mso-bidi-theme-font:minor-latin;mso-fareast-language:\nFR\">Un intervalle est une portion continue de la droite num\u00e9rique. Les\nintervalles sont g\u00e9n\u00e9ralement not\u00e9s sous la forme [a, b], o\u00f9 <span class=\"katex-eq\" data-katex-display=\"false\">a<\/span>\net <span class=\"katex-eq\" data-katex-display=\"false\">b<\/span> sont les extr\u00e9mit\u00e9s de l&rsquo;intervalle. Voici quelques\nexemples d&rsquo;intervalles :<br style=\"mso-special-character:line-break\">\n<br style=\"mso-special-character:line-break\">\n<\/span><\/p>\n\n<p class=\"MsoNormal\"><span style=\"mso-fareast-font-family:&quot;Times New Roman&quot;;\nmso-bidi-font-family:Calibri;mso-bidi-theme-font:minor-latin;mso-fareast-language:\nFR\">&#8211; ]-\u221e, a] : tous les nombres r\u00e9els inf\u00e9rieurs ou \u00e9gaux \u00e0 <span class=\"katex-eq\" data-katex-display=\"false\">a<\/span>.<\/span><\/p>\n\n<p class=\"MsoNormal\"><span style=\"mso-fareast-font-family:&quot;Times New Roman&quot;;\nmso-bidi-font-family:Calibri;mso-bidi-theme-font:minor-latin;mso-fareast-language:\nFR\"><br>\n&#8211; [a, +\u221e[ : tous les nombres r\u00e9els sup\u00e9rieurs ou \u00e9gaux \u00e0 <span class=\"katex-eq\" data-katex-display=\"false\">a<\/span>.<\/span><\/p>\n\n<p class=\"MsoNormal\"><span style=\"mso-fareast-font-family:&quot;Times New Roman&quot;;\nmso-bidi-font-family:Calibri;mso-bidi-theme-font:minor-latin;mso-fareast-language:\nFR\"><br>\n&#8211; ]a, b[ : tous les nombres r\u00e9els strictement entre <span class=\"katex-eq\" data-katex-display=\"false\">a<\/span> et <span class=\"katex-eq\" data-katex-display=\"false\">b<\/span>.<\/span><\/p>\n\n<p class=\"MsoNormal\"><span style=\"mso-fareast-font-family:&quot;Times New Roman&quot;;\nmso-bidi-font-family:Calibri;mso-bidi-theme-font:minor-latin;mso-fareast-language:\nFR\"><br>\n&#8211; [a, b] : tous les nombres r\u00e9els entre <span class=\"katex-eq\" data-katex-display=\"false\">a<\/span> et <span class=\"katex-eq\" data-katex-display=\"false\">b<\/span>,\ninclus.<\/span><\/p>\n\n<p class=\"MsoNormal\"><span style=\"mso-fareast-font-family:&quot;Times New Roman&quot;;\nmso-bidi-font-family:Calibri;mso-bidi-theme-font:minor-latin;mso-fareast-language:\nFR\">&nbsp;<\/span><\/p>\n\n<h2><span class=\"ez-toc-section\" id=\"3_Notation_a_Distance_entre_deux_nombres_reels\"><\/span><span style=\"mso-fareast-font-family:&quot;Times New Roman&quot;;mso-fareast-language:\nFR\">3. Notation |a|. Distance entre deux nombres r\u00e9els :<\/span><span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n<p class=\"MsoNormal\"><span style=\"mso-fareast-font-family:&quot;Times New Roman&quot;;\nmso-bidi-font-family:Calibri;mso-bidi-theme-font:minor-latin;mso-fareast-language:\nFR\">&nbsp;<\/span><\/p>\n\n<p class=\"MsoNormal\"><span style=\"mso-fareast-font-family:&quot;Times New Roman&quot;;\nmso-bidi-font-family:Calibri;mso-bidi-theme-font:minor-latin;mso-fareast-language:\nFR\">La valeur absolue d&rsquo;un nombre r\u00e9el <span class=\"katex-eq\" data-katex-display=\"false\">a<\/span>, not\u00e9e |a|, est la\ndistance entre <span class=\"katex-eq\" data-katex-display=\"false\">a<\/span> et z\u00e9ro sur la droite num\u00e9rique. Pour tout <span class=\"katex-eq\" data-katex-display=\"false\">a<\/span>\ndans <\/span><span style=\"font-family:&quot;Cambria Math&quot;,serif;mso-fareast-font-family:\n&quot;Times New Roman&quot;;mso-bidi-font-family:&quot;Cambria Math&quot;;mso-fareast-language:\nFR\">\u211d<\/span><span style=\"mso-fareast-font-family:&quot;Times New Roman&quot;;mso-bidi-font-family:\nCalibri;mso-bidi-theme-font:minor-latin;mso-fareast-language:FR\">, |a| est\ntoujours positif ou nul.<\/span><\/p>\n\n<p class=\"MsoNormal\"><span style=\"mso-fareast-font-family:&quot;Times New Roman&quot;;\nmso-bidi-font-family:Calibri;mso-bidi-theme-font:minor-latin;mso-fareast-language:\nFR\">&nbsp;<\/span><\/p>\n\n<p class=\"MsoNormal\"><span style=\"mso-fareast-font-family:&quot;Times New Roman&quot;;\nmso-bidi-font-family:Calibri;mso-bidi-theme-font:minor-latin;mso-fareast-language:\nFR\">La distance entre deux nombres r\u00e9els <span class=\"katex-eq\" data-katex-display=\"false\">a<\/span> et <span class=\"katex-eq\" data-katex-display=\"false\">b<\/span>\nest donn\u00e9e par la valeur absolue de leur diff\u00e9rence : |a &#8211; b|.<\/span><\/p>\n\n<p class=\"MsoNormal\"><span style=\"mso-fareast-font-family:&quot;Times New Roman&quot;;\nmso-bidi-font-family:Calibri;mso-bidi-theme-font:minor-latin;mso-fareast-language:\nFR\">&nbsp;<\/span><\/p>\n\n<h2><span class=\"ez-toc-section\" id=\"4_Representation_de_lintervalle_a_%E2%80%93_r_a_r_et_caracterisation_par_la_condition_x_%E2%80%93_a_%E2%A9%BD_r\"><\/span><span style=\"mso-fareast-font-family:&quot;Times New Roman&quot;;mso-fareast-language:\nFR\">4. Repr\u00e9sentation de l&rsquo;intervalle [a &#8211; r, a + r] et caract\u00e9risation par la\ncondition |x &#8211; a| <\/span><span style=\"font-family:&quot;Cambria Math&quot;,serif;\nmso-fareast-font-family:&quot;Times New Roman&quot;;mso-bidi-font-family:&quot;Cambria Math&quot;;\nmso-fareast-language:FR\">\u2a7d<\/span><span style=\"mso-fareast-font-family:&quot;Times New Roman&quot;;\nmso-fareast-language:FR\"> r :<\/span><span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n<p class=\"MsoNormal\"><span style=\"mso-fareast-font-family:&quot;Times New Roman&quot;;\nmso-bidi-font-family:Calibri;mso-bidi-theme-font:minor-latin;mso-fareast-language:\nFR\">&nbsp;<\/span><\/p>\n\n<p class=\"MsoNormal\"><span style=\"mso-fareast-font-family:&quot;Times New Roman&quot;;\nmso-bidi-font-family:Calibri;mso-bidi-theme-font:minor-latin;mso-fareast-language:\nFR\">L&rsquo;intervalle [a &#8211; r, a + r] comprend tous les nombres r\u00e9els situ\u00e9s \u00e0 une\ndistance <span class=\"katex-eq\" data-katex-display=\"false\">r<\/span> ou moins de <span class=\"katex-eq\" data-katex-display=\"false\">a<\/span>. Cela peut \u00eatre\ncaract\u00e9ris\u00e9 par la condition |x &#8211; a| <\/span><span style=\"font-family:&quot;Cambria Math&quot;,serif;\nmso-fareast-font-family:&quot;Times New Roman&quot;;mso-bidi-font-family:&quot;Cambria Math&quot;;\nmso-fareast-language:FR\">\u2a7d<\/span><span style=\"mso-fareast-font-family:&quot;Times New Roman&quot;;\nmso-bidi-font-family:Calibri;mso-bidi-theme-font:minor-latin;mso-fareast-language:\nFR\"> r, qui signifie que la distance entre <span class=\"katex-eq\" data-katex-display=\"false\">x<\/span> et <span class=\"katex-eq\" data-katex-display=\"false\">a<\/span>\nest inf\u00e9rieure ou \u00e9gale \u00e0 <span class=\"katex-eq\" data-katex-display=\"false\">r<\/span>.<\/span><\/p>\n\n<p class=\"MsoNormal\"><span style=\"mso-fareast-font-family:&quot;Times New Roman&quot;;\nmso-bidi-font-family:Calibri;mso-bidi-theme-font:minor-latin;mso-fareast-language:\nFR\">&nbsp;<\/span><\/p>\n\n<h2><span class=\"ez-toc-section\" id=\"5_Ensemble_%F0%9D%94%BB_des_nombres_decimaux_Encadrement_decimal_dun_nombre_reel_a_10_puissance_-n_pres\"><\/span><span style=\"mso-fareast-font-family:&quot;Times New Roman&quot;;mso-fareast-language:\nFR\">5. Ensemble <\/span><span style=\"font-family:&quot;Cambria Math&quot;,serif;\nmso-fareast-font-family:&quot;Times New Roman&quot;;mso-bidi-font-family:&quot;Cambria Math&quot;;\nmso-fareast-language:FR\">\ud835\udd3b<\/span><span style=\"mso-fareast-font-family:\n&quot;Times New Roman&quot;;mso-fareast-language:FR\"> des nombres d\u00e9cimaux. Encadrement\nd\u00e9cimal d&rsquo;un nombre r\u00e9el \u00e0 10 puissance -n pr\u00e8s :<\/span><span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n<p class=\"MsoNormal\"><span style=\"mso-fareast-font-family:&quot;Times New Roman&quot;;\nmso-bidi-font-family:Calibri;mso-bidi-theme-font:minor-latin;mso-fareast-language:\nFR\">&nbsp;<\/span><\/p>\n\n<p class=\"MsoNormal\"><span style=\"mso-fareast-font-family:&quot;Times New Roman&quot;;\nmso-bidi-font-family:Calibri;mso-bidi-theme-font:minor-latin;mso-fareast-language:\nFR\">L&rsquo;ensemble des nombres d\u00e9cimaux, not\u00e9 <\/span><span style=\"font-family:&quot;Cambria Math&quot;,serif;\nmso-fareast-font-family:&quot;Times New Roman&quot;;mso-bidi-font-family:&quot;Cambria Math&quot;;\nmso-fareast-language:FR\">\ud835\udd3b<\/span><span style=\"mso-fareast-font-family:\n&quot;Times New Roman&quot;;mso-bidi-font-family:Calibri;mso-bidi-theme-font:minor-latin;\nmso-fareast-language:FR\">, est constitu\u00e9 de nombres qui peuvent \u00eatre exprim\u00e9s\nsous la forme d&rsquo;une fraction d\u00e9cimale. Pour encadrer un nombre r\u00e9el <span class=\"katex-eq\" data-katex-display=\"false\">x<\/span>\n\u00e0 <span class=\"katex-eq\" data-katex-display=\"false\">10^{-n}<\/span> pr\u00e8s, on cherche deux nombres d\u00e9cimaux <span class=\"katex-eq\" data-katex-display=\"false\">d_1<\/span>\net <span class=\"katex-eq\" data-katex-display=\"false\">d_2<\/span>, tels que <span class=\"katex-eq\" data-katex-display=\"false\">d_1 \\leq x \\leq d_2<\/span>, et dont la\ndiff\u00e9rence est <span class=\"katex-eq\" data-katex-display=\"false\">10^{-n}<\/span> ou moins.<\/span><\/p>\n\n<p class=\"MsoNormal\"><span style=\"mso-fareast-font-family:&quot;Times New Roman&quot;;\nmso-bidi-font-family:Calibri;mso-bidi-theme-font:minor-latin;mso-fareast-language:\nFR\">&nbsp;<\/span><\/p>\n\n<h2><span class=\"ez-toc-section\" id=\"6_Ensemble_%E2%84%9A_des_nombres_rationnels_Nombres_irrationnels\"><\/span><span style=\"mso-fareast-font-family:&quot;Times New Roman&quot;;mso-fareast-language:\nFR\">6. Ensemble <\/span><span style=\"font-family:&quot;Cambria Math&quot;,serif;\nmso-fareast-font-family:&quot;Times New Roman&quot;;mso-bidi-font-family:&quot;Cambria Math&quot;;\nmso-fareast-language:FR\">\u211a<\/span><span style=\"mso-fareast-font-family:&quot;Times New Roman&quot;;\nmso-fareast-language:FR\"> des nombres rationnels. Nombres irrationnels :<\/span><span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n<p class=\"MsoNormal\"><span style=\"mso-fareast-font-family:&quot;Times New Roman&quot;;\nmso-bidi-font-family:Calibri;mso-bidi-theme-font:minor-latin;mso-fareast-language:\nFR\">&nbsp;<\/span><\/p>\n\n<p class=\"MsoNormal\"><span style=\"mso-fareast-font-family:&quot;Times New Roman&quot;;\nmso-bidi-font-family:Calibri;mso-bidi-theme-font:minor-latin;mso-fareast-language:\nFR\">L&rsquo;ensemble des nombres rationnels, not\u00e9 <\/span><span style=\"font-family:\n&quot;Cambria Math&quot;,serif;mso-fareast-font-family:&quot;Times New Roman&quot;;mso-bidi-font-family:\n&quot;Cambria Math&quot;;mso-fareast-language:FR\">\u211a<\/span><span style=\"mso-fareast-font-family:\n&quot;Times New Roman&quot;;mso-bidi-font-family:Calibri;mso-bidi-theme-font:minor-latin;\nmso-fareast-language:FR\">, est compos\u00e9 de tous les nombres qui peuvent \u00eatre\nexprim\u00e9s comme le quotient de deux entiers, avec un d\u00e9nominateur non nul. Les\nnombres irrationnels sont ceux qui ne peuvent pas \u00eatre exprim\u00e9s de cette\nmani\u00e8re.<\/span><\/p>\n\n<p class=\"MsoNormal\"><span style=\"mso-fareast-font-family:&quot;Times New Roman&quot;;\nmso-bidi-font-family:Calibri;mso-bidi-theme-font:minor-latin;mso-fareast-language:\nFR\">&nbsp;<\/span><\/p>\n\n<p class=\"MsoNormal\"><b><span style=\"mso-fareast-font-family:&quot;Times New Roman&quot;;\nmso-bidi-font-family:Calibri;mso-bidi-theme-font:minor-latin;mso-fareast-language:\nFR\">Exemples de nombres irrationnels fournis par la g\u00e9om\u00e9trie :<\/span><\/b><\/p>\n\n<p class=\"MsoNormal\"><b><span style=\"mso-fareast-font-family:&quot;Times New Roman&quot;;\nmso-bidi-font-family:Calibri;mso-bidi-theme-font:minor-latin;mso-fareast-language:\nFR\">&nbsp;<\/span><\/b><\/p>\n\n<p class=\"MsoNormal\"><span style=\"mso-fareast-font-family:&quot;Times New Roman&quot;;\nmso-bidi-font-family:Calibri;mso-bidi-theme-font:minor-latin;mso-fareast-language:\nFR\">&#8211; La racine carr\u00e9e de 2 (<span class=\"katex-eq\" data-katex-display=\"false\"> \\sqrt{2} <\/span>) : Elle provient de la\ndiagonale d&rsquo;un carr\u00e9 de c\u00f4t\u00e9 1. Selon le th\u00e9or\u00e8me de Pythagore, cette longueur\nest <span class=\"katex-eq\" data-katex-display=\"false\"> \\sqrt{2} <\/span>, qui est un nombre irrationnel.<\/span><\/p>\n\n<p class=\"MsoNormal\"><span style=\"mso-fareast-font-family:&quot;Times New Roman&quot;;\nmso-bidi-font-family:Calibri;mso-bidi-theme-font:minor-latin;mso-fareast-language:\nFR\">&#8211; Le nombre \u03c0 (pi) : C&rsquo;est le rapport entre la circonf\u00e9rence d&rsquo;un cercle et\nson diam\u00e8tre. \u03c0 ne peut pas \u00eatre exprim\u00e9 comme le quotient exact de deux\nentiers et est donc irrationnel.<\/span><\/p>\n\n<p class=\"MsoNormal\"><span style=\"mso-fareast-font-family:&quot;Times New Roman&quot;;\nmso-bidi-font-family:Calibri;mso-bidi-theme-font:minor-latin;mso-fareast-language:\nFR\">&nbsp;<\/span><\/p>\n\n<p class=\"MsoNormal\"><span style=\"mso-fareast-font-family:&quot;Times New Roman&quot;;\nmso-bidi-font-family:Calibri;mso-bidi-theme-font:minor-latin;mso-fareast-language:\nFR\">&nbsp;<\/span><\/p>\n\n<h1><span class=\"ez-toc-section\" id=\"Methodes\"><\/span>M\u00e9thodes :<span class=\"ez-toc-section-end\"><\/span><\/h1>\n\n<p class=\"MsoNormal\"><span style=\"mso-fareast-font-family:&quot;Times New Roman&quot;;\nmso-bidi-font-family:Calibri;mso-bidi-theme-font:minor-latin;mso-fareast-language:\nFR\">&nbsp;<\/span><\/p>\n\n<h2><span class=\"ez-toc-section\" id=\"1_Associer_a_chaque_point_de_la_droite_graduee_un_unique_nombre_reel_et_reciproquement\"><\/span><span style=\"mso-fareast-font-family:&quot;Times New Roman&quot;;mso-fareast-language:\nFR\">1. Associer \u00e0 chaque point de la droite gradu\u00e9e un unique nombre r\u00e9el et r\u00e9ciproquement\n:<\/span><span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n<p class=\"MsoNormal\"><span style=\"mso-fareast-font-family:&quot;Times New Roman&quot;;\nmso-bidi-font-family:Calibri;mso-bidi-theme-font:minor-latin;mso-fareast-language:\nFR\"><span style=\"mso-spacerun:yes\">&nbsp;&nbsp; <\/span><\/span><\/p>\n\n<p class=\"MsoNormal\"><span style=\"mso-fareast-font-family:&quot;Times New Roman&quot;;\nmso-bidi-font-family:Calibri;mso-bidi-theme-font:minor-latin;mso-fareast-language:\nFR\"><span style=\"mso-spacerun:yes\">&nbsp;&nbsp; <\/span>&#8211; <b>Associer un nombre r\u00e9el \u00e0 un\npoint :<\/b><\/span><\/p>\n\n<p class=\"MsoNormal\"><span style=\"mso-fareast-font-family:&quot;Times New Roman&quot;;\nmso-bidi-font-family:Calibri;mso-bidi-theme-font:minor-latin;mso-fareast-language:\nFR\">&nbsp;<\/span><\/p>\n\n<p class=\"MsoNormal\"><span style=\"mso-fareast-font-family:&quot;Times New Roman&quot;;\nmso-bidi-font-family:Calibri;mso-bidi-theme-font:minor-latin;mso-fareast-language:\nFR\"><span style=\"mso-spacerun:yes\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <\/span>Pour tout point\n<span class=\"katex-eq\" data-katex-display=\"false\">P<\/span> sur la droite gradu\u00e9e, on mesure la distance entre\n<span class=\"katex-eq\" data-katex-display=\"false\">P<\/span> et l&rsquo;origine <span class=\"katex-eq\" data-katex-display=\"false\">O<\/span>, qui repr\u00e9sente le nombre 0. Si\n<span class=\"katex-eq\" data-katex-display=\"false\">P<\/span> est \u00e0 droite de <span class=\"katex-eq\" data-katex-display=\"false\">O<\/span>, le nombre associ\u00e9 est\npositif, et s&rsquo;il est \u00e0 gauche, le nombre est n\u00e9gatif. La distance mesure la\nvaleur absolue du nombre.<\/span><\/p>\n\n<p class=\"MsoNormal\"><span style=\"mso-fareast-font-family:&quot;Times New Roman&quot;;\nmso-bidi-font-family:Calibri;mso-bidi-theme-font:minor-latin;mso-fareast-language:\nFR\"><span style=\"mso-spacerun:yes\">&nbsp;&nbsp; <\/span><\/span><\/p>\n\n<p class=\"MsoNormal\"><span style=\"mso-fareast-font-family:&quot;Times New Roman&quot;;\nmso-bidi-font-family:Calibri;mso-bidi-theme-font:minor-latin;mso-fareast-language:\nFR\"><span style=\"mso-spacerun:yes\">&nbsp;&nbsp; <\/span>&#8211; <b>Associer un point \u00e0 un nombre\nr\u00e9el :<br style=\"mso-special-character:line-break\">\n<br style=\"mso-special-character:line-break\">\n<\/b><\/span><\/p>\n\n<p class=\"MsoNormal\"><span style=\"mso-fareast-font-family:&quot;Times New Roman&quot;;\nmso-bidi-font-family:Calibri;mso-bidi-theme-font:minor-latin;mso-fareast-language:\nFR\"><span style=\"mso-spacerun:yes\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <\/span>Pour placer un nombre r\u00e9el\n<span class=\"katex-eq\" data-katex-display=\"false\">a<\/span> sur la droite, on part de l&rsquo;origine <span class=\"katex-eq\" data-katex-display=\"false\">O<\/span>. Si\n<span class=\"katex-eq\" data-katex-display=\"false\">a<\/span> est positif, on se d\u00e9place vers la droite de\n<span class=\"katex-eq\" data-katex-display=\"false\">|a|<\/span> unit\u00e9s pour marquer le point <span class=\"katex-eq\" data-katex-display=\"false\">P<\/span>. Si\n<span class=\"katex-eq\" data-katex-display=\"false\">a<\/span> est n\u00e9gatif, on se d\u00e9place vers la gauche de <span class=\"katex-eq\" data-katex-display=\"false\">|a|<\/span>\nunit\u00e9s.<\/span><\/p>\n\n<p class=\"MsoNormal\"><span style=\"mso-fareast-font-family:&quot;Times New Roman&quot;;\nmso-bidi-font-family:Calibri;mso-bidi-theme-font:minor-latin;mso-fareast-language:\nFR\">&nbsp;<\/span><\/p>\n\n<h2><span class=\"ez-toc-section\" id=\"2_Representer_un_intervalle_de_la_droite_numerique_et_determiner_si_un_nombre_reel_appartient_a_un_intervalle_donne\"><\/span><span style=\"mso-fareast-font-family:&quot;Times New Roman&quot;;mso-fareast-language:\nFR\">2. Repr\u00e9senter un intervalle de la droite num\u00e9rique et d\u00e9terminer si un\nnombre r\u00e9el appartient \u00e0 un intervalle donn\u00e9 :<\/span><span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n<p class=\"MsoNormal\"><span style=\"mso-fareast-font-family:&quot;Times New Roman&quot;;\nmso-bidi-font-family:Calibri;mso-bidi-theme-font:minor-latin;mso-fareast-language:\nFR\">&nbsp;<\/span><\/p>\n\n<p class=\"MsoNormal\"><span style=\"mso-fareast-font-family:&quot;Times New Roman&quot;;\nmso-bidi-font-family:Calibri;mso-bidi-theme-font:minor-latin;mso-fareast-language:\nFR\"><span style=\"mso-spacerun:yes\">&nbsp;&nbsp; <\/span>&#8211; <b>Repr\u00e9senter un intervalle :<br style=\"mso-special-character:line-break\">\n<br style=\"mso-special-character:line-break\">\n<\/b><\/span><\/p>\n\n<p class=\"MsoNormal\"><span style=\"mso-fareast-font-family:&quot;Times New Roman&quot;;\nmso-bidi-font-family:Calibri;mso-bidi-theme-font:minor-latin;mso-fareast-language:\nFR\"><span style=\"mso-spacerun:yes\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <\/span>Pour repr\u00e9senter un intervalle,\npar exemple <span class=\"katex-eq\" data-katex-display=\"false\">a, b<\/span>, on marque les points correspondant \u00e0\n<span class=\"katex-eq\" data-katex-display=\"false\">a<\/span> et <span class=\"katex-eq\" data-katex-display=\"false\">b<\/span> sur la droite num\u00e9rique et on dessine un\nsegment de ligne les reliant. On utilise des crochets <span class=\"katex-eq\" data-katex-display=\"false\"> <\/span> pour\nindiquer que les points <span class=\"katex-eq\" data-katex-display=\"false\">a<\/span> et <span class=\"katex-eq\" data-katex-display=\"false\">b<\/span> sont inclus dans\nl&rsquo;intervalle, et des parenth\u00e8ses <span class=\"katex-eq\" data-katex-display=\"false\"> ( ) <\/span> pour indiquer qu&rsquo;ils sont\nexclus.<\/span><\/p>\n\n<p class=\"MsoNormal\"><span style=\"mso-fareast-font-family:&quot;Times New Roman&quot;;\nmso-bidi-font-family:Calibri;mso-bidi-theme-font:minor-latin;mso-fareast-language:\nFR\">&nbsp;<\/span><\/p>\n\n<p class=\"MsoNormal\"><span style=\"mso-fareast-font-family:&quot;Times New Roman&quot;;\nmso-bidi-font-family:Calibri;mso-bidi-theme-font:minor-latin;mso-fareast-language:\nFR\"><span style=\"mso-spacerun:yes\">&nbsp;&nbsp; <\/span>&#8211; <b>V\u00e9rifier l&rsquo;appartenance \u00e0 un\nintervalle :<br style=\"mso-special-character:line-break\">\n<br style=\"mso-special-character:line-break\">\n<\/b><\/span><\/p>\n\n<p class=\"MsoNormal\"><span style=\"mso-fareast-font-family:&quot;Times New Roman&quot;;\nmso-bidi-font-family:Calibri;mso-bidi-theme-font:minor-latin;mso-fareast-language:\nFR\"><span style=\"mso-spacerun:yes\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <\/span>Pour v\u00e9rifier si un nombre r\u00e9el\n<span class=\"katex-eq\" data-katex-display=\"false\">x<\/span> appartient \u00e0 un intervalle <span class=\"katex-eq\" data-katex-display=\"false\">a, b<\/span>, on v\u00e9rifie\nsimplement si <span class=\"katex-eq\" data-katex-display=\"false\">a \\leq x \\leq b<\/span>. Si c&rsquo;est le cas, alors\n<span class=\"katex-eq\" data-katex-display=\"false\">x<\/span> appartient \u00e0 l&rsquo;intervalle.<\/span><\/p>\n\n<p class=\"MsoNormal\"><span style=\"mso-fareast-font-family:&quot;Times New Roman&quot;;\nmso-bidi-font-family:Calibri;mso-bidi-theme-font:minor-latin;mso-fareast-language:\nFR\">&nbsp;<\/span><\/p>\n\n<h2><span class=\"ez-toc-section\" id=\"3_Donner_un_encadrement_damplitude_donnee_dun_nombre_reel_par_des_decimaux\"><\/span><span style=\"mso-fareast-font-family:&quot;Times New Roman&quot;;mso-fareast-language:\nFR\">3. Donner un encadrement, d&rsquo;amplitude donn\u00e9e, d\u2019un nombre r\u00e9el par des\nd\u00e9cimaux :<\/span><span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n<p class=\"MsoNormal\"><span style=\"mso-fareast-font-family:&quot;Times New Roman&quot;;\nmso-bidi-font-family:Calibri;mso-bidi-theme-font:minor-latin;mso-fareast-language:\nFR\">&nbsp;<\/span><\/p>\n\n<p class=\"MsoNormal\"><span style=\"mso-fareast-font-family:&quot;Times New Roman&quot;;\nmso-bidi-font-family:Calibri;mso-bidi-theme-font:minor-latin;mso-fareast-language:\nFR\"><span style=\"mso-spacerun:yes\">&nbsp;&nbsp; <\/span>Pour encadrer un nombre r\u00e9el\n<span class=\"katex-eq\" data-katex-display=\"false\">x<\/span> avec une amplitude donn\u00e9e, par exemple <span class=\"katex-eq\" data-katex-display=\"false\">10^{-n}<\/span>,\non cherche deux nombres d\u00e9cimaux <span class=\"katex-eq\" data-katex-display=\"false\">d_1<\/span> et <span class=\"katex-eq\" data-katex-display=\"false\">d_2<\/span> tels\nque <span class=\"katex-eq\" data-katex-display=\"false\">d_1 \\leq x \\leq d_2<\/span> et que la diff\u00e9rence <span class=\"katex-eq\" data-katex-display=\"false\">d_2 &#8211;\nd_1<\/span> soit inf\u00e9rieure ou \u00e9gale \u00e0 <span class=\"katex-eq\" data-katex-display=\"false\">10^{-n}<\/span>. En pratique,\ncela revient souvent \u00e0 arrondir <span class=\"katex-eq\" data-katex-display=\"false\">x<\/span> \u00e0 <span class=\"katex-eq\" data-katex-display=\"false\">n<\/span> d\u00e9cimales\npour obtenir <span class=\"katex-eq\" data-katex-display=\"false\">d_1<\/span> et <span class=\"katex-eq\" data-katex-display=\"false\">d_2<\/span>.<\/span><\/p>\n\n<p class=\"MsoNormal\"><span style=\"mso-fareast-font-family:&quot;Times New Roman&quot;;\nmso-bidi-font-family:Calibri;mso-bidi-theme-font:minor-latin;mso-fareast-language:\nFR\">&nbsp;<\/span><\/p>\n\n<h2><span class=\"ez-toc-section\" id=\"4_Arrondir_en_donnant_le_nombre_de_chiffres_significatifs_adapte_a_la_situation_etudiee\"><\/span><span style=\"mso-fareast-font-family:&quot;Times New Roman&quot;;mso-fareast-language:\nFR\">4. Arrondir en donnant le nombre de chiffres significatifs adapt\u00e9 \u00e0 la\nsituation \u00e9tudi\u00e9e :<\/span><span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n<p class=\"MsoNormal\"><span style=\"mso-fareast-font-family:&quot;Times New Roman&quot;;\nmso-bidi-font-family:Calibri;mso-bidi-theme-font:minor-latin;mso-fareast-language:\nFR\">&nbsp;<\/span><\/p>\n\n<p class=\"MsoNormal\"><span style=\"mso-fareast-font-family:&quot;Times New Roman&quot;;\nmso-bidi-font-family:Calibri;mso-bidi-theme-font:minor-latin;mso-fareast-language:\nFR\"><span style=\"mso-spacerun:yes\">&nbsp;&nbsp; <\/span>Lors de la r\u00e9solution de\nprobl\u00e8mes, il est important d&rsquo;arrondir les r\u00e9ponses de mani\u00e8re appropri\u00e9e \u00e0 la\nsituation. Le nombre de chiffres significatifs doit \u00eatre d\u00e9termin\u00e9 en fonction\nde la pr\u00e9cision des donn\u00e9es d&rsquo;entr\u00e9e et du contexte du probl\u00e8me.<\/span><\/p>\n\n<p class=\"MsoNormal\"><span style=\"mso-fareast-font-family:&quot;Times New Roman&quot;;\nmso-bidi-font-family:Calibri;mso-bidi-theme-font:minor-latin;mso-fareast-language:\nFR\"><span style=\"mso-spacerun:yes\">&nbsp;&nbsp; <\/span><\/span><\/p>\n\n<p class=\"MsoNormal\"><span style=\"mso-fareast-font-family:&quot;Times New Roman&quot;;\nmso-bidi-font-family:Calibri;mso-bidi-theme-font:minor-latin;mso-fareast-language:\nFR\"><span style=\"mso-spacerun:yes\">&nbsp;&nbsp; <\/span>&#8211; <b>Identifier la pr\u00e9cision\nrequise :<\/b> Examinez les donn\u00e9es du probl\u00e8me pour d\u00e9terminer le niveau de\npr\u00e9cision requis.<br style=\"mso-special-character:line-break\">\n<br style=\"mso-special-character:line-break\">\n<\/span><\/p>\n\n<p class=\"MsoNormal\"><span style=\"mso-fareast-font-family:&quot;Times New Roman&quot;;\nmso-bidi-font-family:Calibri;mso-bidi-theme-font:minor-latin;mso-fareast-language:\nFR\"><span style=\"mso-spacerun:yes\">&nbsp;&nbsp; <\/span>&#8211; <b>Arrondir de mani\u00e8re\nappropri\u00e9e<\/b> : Arrondissez votre r\u00e9ponse finale \u00e0 ce nombre de chiffres\nsignificatifs, en vous assurant de conserver la pr\u00e9cision tout en \u00e9vitant une\nfausse impression de certitude.<\/span><\/p>\n\n<p class=\"MsoNormal\"><span style=\"mso-fareast-font-family:&quot;Times New Roman&quot;;\nmso-bidi-font-family:Calibri;mso-bidi-theme-font:minor-latin;mso-fareast-language:\nFR\">&nbsp;<\/span><\/p>\n\n<p class=\"MsoNormal\"><span style=\"mso-fareast-font-family:&quot;Times New Roman&quot;;\nmso-bidi-font-family:Calibri;mso-bidi-theme-font:minor-latin;mso-fareast-language:\nFR\">Par exemple, si vous mesurez une longueur avec une r\u00e8gle gradu\u00e9e au\nmillim\u00e8tre, il n&rsquo;est pas logique de donner une r\u00e9ponse \u00e0 six d\u00e9cimales. De\nm\u00eame, si une question concerne des personnes, la r\u00e9ponse doit \u00eatre un entier.<\/span><\/p>\n\n<p class=\"MsoNormal\"><span style=\"mso-fareast-font-family:&quot;Times New Roman&quot;;\nmso-bidi-font-family:Calibri;mso-bidi-theme-font:minor-latin;mso-fareast-language:\nFR\">&nbsp;<\/span><\/p>\n\n<p class=\"MsoNormal\"><span style=\"mso-fareast-font-family:&quot;Times New Roman&quot;;\nmso-bidi-font-family:Calibri;mso-bidi-theme-font:minor-latin;mso-fareast-language:\nFR\">Ces m\u00e9thodes sont des outils essentiels pour manipuler et interpr\u00e9ter les\nnombres r\u00e9els dans divers contextes math\u00e9matiques et scientifiques.<\/span><\/p>\n\n\n\n\n\n<style>@font-face\n\t{font-family:\"Cambria Math\";\n\tpanose-1:2 4 5 3 5 4 6 3 2 4;\n\tmso-font-charset:0;\n\tmso-generic-font-family:roman;\n\tmso-font-pitch:variable;\n\tmso-font-signature:-536870145 1107305727 0 0 415 0;}@font-face\n\t{font-family:Calibri;\n\tpanose-1:2 15 5 2 2 2 4 3 2 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Roman\";\n\tmso-bidi-theme-font:minor-bidi;\n\tmso-fareast-language:EN-US;}div.WordSection1\n\t{page:WordSection1;}<\/style>\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<section class=\"elementor-section elementor-top-section elementor-element elementor-element-071e74f elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"071e74f\" data-element_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-100 elementor-top-column elementor-element elementor-element-8c43dc4\" data-id=\"8c43dc4\" data-element_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-aa0c527 elementor-widget elementor-widget-spacer\" data-id=\"aa0c527\" data-element_type=\"widget\" data-widget_type=\"spacer.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-spacer\">\n\t\t\t<div class=\"elementor-spacer-inner\"><\/div>\n\t\t<\/div>\n\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<section class=\"elementor-section elementor-top-section elementor-element elementor-element-789777a elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"789777a\" data-element_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-100 elementor-top-column elementor-element elementor-element-dd93843\" data-id=\"dd93843\" data-element_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\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-b1d0d5c elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"b1d0d5c\" data-element_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-100 elementor-top-column elementor-element elementor-element-7e963bc\" data-id=\"7e963bc\" data-element_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\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-40909d1 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"40909d1\" data-element_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-100 elementor-top-column elementor-element elementor-element-3a01f62\" data-id=\"3a01f62\" data-element_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\t<\/div>\n\t\t<\/section>\n\t\t\t\t<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"<p>Manipuler les nombres r\u00e9els Introduction &nbsp; La manipulation des nombres r\u00e9els est essentielle dans divers domaines des math\u00e9matiques et de la science. Comprendre les caract\u00e9ristiques des diff\u00e9rents sous-ensembles de \u211d, tels que \u211a, \ud835\udd3b, et les nombres irrationnels, ainsi que les notions d&rsquo;intervalle et de distance, est crucial pour travailler efficacement avec les nombres r\u00e9els. [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"elementor_canvas","format":"standard","meta":{"footnotes":""},"categories":[25,26,5],"tags":[],"_links":{"self":[{"href":"https:\/\/www.maxdecours.com\/maxblog\/wp-json\/wp\/v2\/posts\/1877"}],"collection":[{"href":"https:\/\/www.maxdecours.com\/maxblog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.maxdecours.com\/maxblog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.maxdecours.com\/maxblog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.maxdecours.com\/maxblog\/wp-json\/wp\/v2\/comments?post=1877"}],"version-history":[{"count":14,"href":"https:\/\/www.maxdecours.com\/maxblog\/wp-json\/wp\/v2\/posts\/1877\/revisions"}],"predecessor-version":[{"id":2012,"href":"https:\/\/www.maxdecours.com\/maxblog\/wp-json\/wp\/v2\/posts\/1877\/revisions\/2012"}],"wp:attachment":[{"href":"https:\/\/www.maxdecours.com\/maxblog\/wp-json\/wp\/v2\/media?parent=1877"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.maxdecours.com\/maxblog\/wp-json\/wp\/v2\/categories?post=1877"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.maxdecours.com\/maxblog\/wp-json\/wp\/v2\/tags?post=1877"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}