{"id":22417,"date":"2022-10-19T08:21:25","date_gmt":"2022-10-19T07:21:25","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=22417"},"modified":"2022-10-19T09:21:57","modified_gmt":"2022-10-19T08:21:57","slug":"considera-os-numeros-seguintes","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=22417","title":{"rendered":"Representa na forma de fra\u00e7\u00e3o"},"content":{"rendered":"\n<p><ul id='GTTabs_ul_22417' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_22417' class='GTTabs_curr'><a  id=\"22417_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_22417' ><a  id=\"22417_1\" onMouseOver=\"GTTabsShowLinks('Resolu\u00e7\u00e3o'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Resolu\u00e7\u00e3o<\/a><\/li>\n<\/ul>\n\n<div class='GTTabs_divs GTTabs_curr_div' id='GTTabs_0_22417'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>Representa na forma de fra\u00e7\u00e3o os n\u00fameros racionais \\(2,\\left( {36} \\right)\\) e \\(0,7\\left( 2 \\right)\\).<\/p>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_22417' onClick='GTTabs_show(1,22417)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_22417'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<p>Designando a d\u00edzima por \\(x\\), vem: \\(x = 2,\\left( {36} \\right)\\).<br \/>Logo, multiplicando por \\(100\\) os dois membros da igualdade anterior, vem: \\(100x = 236,\\left( {36} \\right)\\).<br \/>Subtraindo, membro a membro, as duas equa\u00e7\u00f5es anteriores, temos:<br \/>\\[\\begin{array}{*{20}{r}}{}&amp;{100x}&amp; = &amp;{236,\\left( {36} \\right)}\\\\ &#8211; &amp;x&amp; = &amp;{2,\\left( {36} \\right)}\\\\\\hline{}&amp;{99x}&amp; = &amp;{234\\quad\\quad\\,}\\end{array}\\]<br \/>Donde, \\(x = \\frac{{234}}{{99}} = \\frac{{26}}{{11}}\\).<br \/>Portanto, \\(2,\\left( {36} \\right) = \\frac{{26}}{{11}}\\).<\/p>\n<p>\u00a0<\/p>\n<p>Designando a d\u00edzima por \\(x\\), vem: \\(x = 0,7\\left( 2 \\right)\\).<br \/>Logo, multiplicando por \\(10\\) e por \\({100}\\) os dois membros da igualdade anterior, vem: \\(10x = 7,\\left( 2 \\right)\\) e \\(100x = 72,\\left( 2 \\right)\\), respetivamente.<br \/>Subtraindo, membro a membro, as duas equa\u00e7\u00f5es anteriores, temos:<br \/>\\[\\begin{array}{*{20}{r}}{}&amp;{100x}&amp; = &amp;{72,\\left( 2 \\right)}\\\\ &#8211; &amp;{10x}&amp; = &amp;{7,\\left( 2 \\right)}\\\\\\hline{}&amp;{90x}&amp; = &amp;{65\\quad\\;\\;\\,}\\end{array}\\]<br \/>Donde, \\(x = \\frac{{65}}{{90}} = \\frac{{13}}{{18}}\\).<br \/>Portanto, \\(0,7\\left( 2 \\right) = \\frac{{13}}{{18}}\\).<\/p>\n\n\n\n<p><\/p>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_22417' onClick='GTTabs_show(0,22417)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Representa na forma de fra\u00e7\u00e3o os n\u00fameros racionais \\(2,\\left( {36} \\right)\\) e \\(0,7\\left( 2 \\right)\\). Resolu\u00e7\u00e3o &gt;&gt; Resolu\u00e7\u00e3o &lt;&lt; Enunciado<\/p>\n","protected":false},"author":1,"featured_media":14114,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[100,664],"tags":[424,261,666],"series":[],"class_list":["post-22417","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-8--ano","category-numeros-reais","tag-8-o-ano","tag-dizima","tag-dizima-infinita-periodica"],"views":276,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/Mat56.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/22417","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=22417"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/22417\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/14114"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=22417"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=22417"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=22417"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=22417"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}