{"id":2490,"date":"2019-09-03T20:39:13","date_gmt":"2019-09-03T18:39:13","guid":{"rendered":"http:\/\/jhmaths.fr\/?page_id=2490"},"modified":"2024-12-06T09:52:52","modified_gmt":"2024-12-06T08:52:52","slug":"information-chiffree","status":"publish","type":"page","link":"https:\/\/jhmaths.fr\/index.php\/seconde\/information-chiffree\/","title":{"rendered":"Information chiffr\u00e9e"},"content":{"rendered":"\n<h2 class=\"wp-block-heading\">Proportions, pourcentages<\/h2>\n\n\n\n<p class=\"propriete wp-block-paragraph\"><strong>Calculer une proportion<\/strong> :<br><br>La proportion d&rsquo;une sous-population \\(N_A\\) dans une population \\(N_E\\) s&rsquo;\u00e9crit $f=\\frac{N_A}{N_E} \\hspace{10px} \\left(= \\frac{\\text{effectif}}{\\text{effectif total}}\\right)$, exprim\u00e9e plut\u00f4t en nombre d\u00e9cimal, mais aussi en fraction ou en pourcentage.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span class=\"proprieteseconde\"><\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Exemple<\/strong> :<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><tbody><tr><td class=\"has-text-align-center\" data-align=\"center\">V\u00e9hicule<\/td><td class=\"has-text-align-center\" data-align=\"center\">Train<\/td><td class=\"has-text-align-center\" data-align=\"center\">Bus<\/td><td class=\"has-text-align-center\" data-align=\"center\">Voiture<\/td><td class=\"has-text-align-center\" data-align=\"center\"><strong>Total<\/strong><\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">Effectif<\/td><td class=\"has-text-align-center\" data-align=\"center\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-accent-3-color\"><strong>73<\/strong><\/mark><\/td><td class=\"has-text-align-center\" data-align=\"center\">28<\/td><td class=\"has-text-align-center\" data-align=\"center\">14<\/td><td class=\"has-text-align-center\" data-align=\"center\"><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-accent-3-color\">115<\/mark><\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">La fr\u00e9quence d&rsquo;usagers du train vaut $\\dfrac{73}{115}\\approx 0,635 \\hspace{10px} (=63,5 \\%) $<\/p>\n\n\n\n<div style=\"height:100px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<h3 class=\"wp-block-heading\">Quizz<\/h3>\n\n\n<div class=\"h5p-iframe-wrapper\"><iframe id=\"h5p-iframe-27\" class=\"h5p-iframe\" data-content-id=\"27\" style=\"height:1px\" src=\"about:blank\" frameBorder=\"0\" scrolling=\"no\" title=\"2nde - Pourcentages - Calculer une proportion\"><\/iframe><\/div>\n\n\n\n<div style=\"height:100px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<p class=\"propriete wp-block-paragraph\"><span class=\"proprieteseconde\"><strong>Pourcentage de pourcentage<\/strong><\/span> :<br><br><span class=\"proprieteseconde\">Pour calculer un pourcentage \\(p\\) d&rsquo;une quantit\u00e9 $Q$ ou d&rsquo;un autre pourcentage, on les multiplie (\\(p \\times Q\\) ou \\(p_1 \\times p_2\\) &#8230; )<\/span><\/p>\n\n\n\n<div style=\"height:100px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<h3 class=\"wp-block-heading\">Quizz<\/h3>\n\n\n<div class=\"h5p-iframe-wrapper\"><iframe id=\"h5p-iframe-28\" class=\"h5p-iframe\" data-content-id=\"28\" style=\"height:1px\" src=\"about:blank\" frameBorder=\"0\" scrolling=\"no\" title=\"2nde - Pourcentages - Pourcentages de pourcentages\"><\/iframe><\/div>\n\n\n\n<div style=\"height:100px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<h2 class=\"wp-block-heading\">\u00c9volutions<\/h2>\n\n\n\n<p class=\"propriete wp-block-paragraph\"><strong><span class=\"proprieteseconde\">Coefficients multiplicateurs<\/span> :<\/strong><br><br><span class=\"proprieteseconde\">Pour calculer le taux de variation (relative) entre deux quantit\u00e9s \\(V_1\\) et \\(V_2\\), on calcule $ \\dfrac{V_2-V_1}{V_1}$<\/span><br><br><span class=\"proprieteseconde\">Augmenter une quantit\u00e9 de \\(p\\) % revient \u00e0 la multiplier par le coefficient multiplicateur \\(c_m=1+\\frac{p}{100}\\)<\/span><br><br><span class=\"proprieteseconde\">Diminuer une quantit\u00e9 de \\(p\\) % revient \u00e0 la multiplier par le coefficient multiplicateur \\(c_m=1-\\frac{p}{100}\\)<\/span><\/p>\n\n\n\n<div style=\"height:100px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<h3 class=\"wp-block-heading\">Quizz<\/h3>\n\n\n<div class=\"h5p-iframe-wrapper\"><iframe id=\"h5p-iframe-29\" class=\"h5p-iframe\" data-content-id=\"29\" style=\"height:1px\" src=\"about:blank\" frameBorder=\"0\" scrolling=\"no\" title=\"2nde - Pourcentages - \u00e9volutions\"><\/iframe><\/div>\n\n\n\n<div style=\"height:100px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<figure class=\"wp-block-embed is-type-rich is-provider-prise-en-charge-des-contenus-embarqu-s wp-block-embed-prise-en-charge-des-contenus-embarqu-s wp-embed-aspect-16-9 wp-has-aspect-ratio\"><div class=\"wp-block-embed__wrapper\">\n<iframe loading=\"lazy\" title=\"Calculer un coefficient multiplicateur (taux d&#039;\u00e9volution) - Seconde\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/-5QmcMuzy5I?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe>\n<\/div><\/figure>\n\n\n\n<div style=\"height:100px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<p class=\"propriete wp-block-paragraph\"><strong><span class=\"proprieteseconde\">\u00c9volutions successives et taux global<\/span> :<\/strong><br><span class=\"proprieteseconde\">Pour calculer plusieurs \u00e9volutions successives on multiplie les coefficients multiplicateurs entre eux. (\\(c_1 \\times c_2 \\times \\dots \\))<\/span><\/p>\n\n\n\n<div style=\"height:100px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<figure class=\"wp-block-embed is-type-rich is-provider-prise-en-charge-des-contenus-embarqu-s wp-block-embed-prise-en-charge-des-contenus-embarqu-s wp-embed-aspect-16-9 wp-has-aspect-ratio\"><div class=\"wp-block-embed__wrapper\">\n<iframe loading=\"lazy\" title=\"Calculer des taux d&#039;\u00e9volution successifs - Seconde\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/qOg2eXd8Hv0?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe>\n<\/div><\/figure>\n\n\n\n<div style=\"height:100px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<h3 class=\"wp-block-heading\">Quizz<\/h3>\n\n\n<div class=\"h5p-iframe-wrapper\"><iframe id=\"h5p-iframe-31\" class=\"h5p-iframe\" data-content-id=\"31\" style=\"height:1px\" src=\"about:blank\" frameBorder=\"0\" scrolling=\"no\" title=\"2nde - Pourcentages - \u00e9volutions successives\"><\/iframe><\/div>\n\n\n\n<div style=\"height:100px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<p class=\"propriete wp-block-paragraph\"><strong><span class=\"proprieteseconde\">Taux r\u00e9ciproque<\/span> :<\/strong><br><span class=\"proprieteseconde\">Apr\u00e8s une \u00e9volution de coefficient \\(c\\) d&rsquo;une quantit\u00e9 de d\u00e9part , l&rsquo;\u00e9volution n\u00e9cessaire pour y revenir a pour coefficient \\(\\frac{1}{c}\\)<\/span><\/p>\n\n\n\n<div style=\"height:100px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<figure class=\"wp-block-embed is-type-rich is-provider-prise-en-charge-des-contenus-embarqu-s wp-block-embed-prise-en-charge-des-contenus-embarqu-s wp-embed-aspect-16-9 wp-has-aspect-ratio\"><div class=\"wp-block-embed__wrapper\">\n<iframe loading=\"lazy\" title=\"Calculer un taux d&#039;\u00e9volution r\u00e9ciproque - Seconde\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/NiCxHYkpNiM?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe>\n<\/div><\/figure>\n\n\n\n<div style=\"height:100px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<h3 class=\"wp-block-heading\">Quizz<\/h3>\n\n\n<div class=\"h5p-iframe-wrapper\"><iframe id=\"h5p-iframe-32\" class=\"h5p-iframe\" data-content-id=\"32\" style=\"height:1px\" src=\"about:blank\" frameBorder=\"0\" scrolling=\"no\" title=\"2nde - Pourcentages - taux r\u00e9ciproque\"><\/iframe><\/div>\n","protected":false},"excerpt":{"rendered":"<p>Proportions, pourcentages Calculer une proportion : La proportion d&rsquo;une sous-population \\(N_A\\) dans une population \\(N_E\\) s&rsquo;\u00e9crit $f=\\frac{N_A}{N_E} \\hspace{10px} \\left(= \\frac{\\text{effectif}}{\\text{effectif total}}\\right)$, exprim\u00e9e plut\u00f4t en nombre d\u00e9cimal, mais aussi en fraction ou en pourcentage. Exemple : V\u00e9hicule Train Bus Voiture Total Effectif 73 28 14 115 La fr\u00e9quence d&rsquo;usagers du train vaut $\\dfrac{73}{115}\\approx 0,635 \\hspace{10px} (=63,5 [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":2085,"menu_order":7,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"folder":[],"class_list":["post-2490","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/jhmaths.fr\/index.php\/wp-json\/wp\/v2\/pages\/2490","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/jhmaths.fr\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/jhmaths.fr\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/jhmaths.fr\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/jhmaths.fr\/index.php\/wp-json\/wp\/v2\/comments?post=2490"}],"version-history":[{"count":33,"href":"https:\/\/jhmaths.fr\/index.php\/wp-json\/wp\/v2\/pages\/2490\/revisions"}],"predecessor-version":[{"id":3989,"href":"https:\/\/jhmaths.fr\/index.php\/wp-json\/wp\/v2\/pages\/2490\/revisions\/3989"}],"up":[{"embeddable":true,"href":"https:\/\/jhmaths.fr\/index.php\/wp-json\/wp\/v2\/pages\/2085"}],"wp:attachment":[{"href":"https:\/\/jhmaths.fr\/index.php\/wp-json\/wp\/v2\/media?parent=2490"}],"wp:term":[{"taxonomy":"folder","embeddable":true,"href":"https:\/\/jhmaths.fr\/index.php\/wp-json\/wp\/v2\/folder?post=2490"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}