{"id":22428,"date":"2022-10-19T09:26:58","date_gmt":"2022-10-19T08:26:58","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=22428"},"modified":"2022-10-19T13:30:22","modified_gmt":"2022-10-19T12:30:22","slug":"considera-os-numeros-seguintes-2","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=22428","title":{"rendered":"Considera os n\u00fameros seguintes"},"content":{"rendered":"\n<p><ul id='GTTabs_ul_22428' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_22428' class='GTTabs_curr'><a  id=\"22428_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_22428' ><a  id=\"22428_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_22428'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>Considera os n\u00fameros seguintes:<\/p>\n<p>\\[\\begin{array}{*{20}{l}}{\\frac{6}{7}}&amp;{ &#8211; \\frac{{17}}{6}}&amp;{ &#8211; \\frac{{15}}{9}}&amp;{\\frac{7}{5}}&amp;{ &#8211; \\frac{{13}}{{52}}}\\end{array}\\]<\/p>\n<ol style=\"list-style-type: lower-alpha;\">\n<li>Indica as fra\u00e7\u00f5es que se podem representar em d\u00edzima finita, identificando as fra\u00e7\u00f5es equivalentes a fra\u00e7\u00f5es decimais. Escreve essas fra\u00e7\u00f5es decimais.<\/li>\n<li>Escreve a representa\u00e7\u00e3o em d\u00edzima de cada um dos n\u00fameros.<\/li>\n<li>Identifica o per\u00edodo, e o respetivo comprimento, das d\u00edzimas infinitas peri\u00f3dicas escritas na al\u00ednea anterior.<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_22428' onClick='GTTabs_show(1,22428)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_22428'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<table style=\"border-collapse: collapse;\">\n<tbody>\n<tr>\n<td>\u00a0<\/td>\n<td>\u00a0<\/td>\n<td>Fra\u00e7\u00e3o equivalente a fra\u00e7\u00e3o decimal<\/td>\n<td>D\u00edzima finita<\/td>\n<td>D\u00edzima infinita peri\u00f3dica<\/td>\n<\/tr>\n<tr>\n<td>A<\/td>\n<td>\\[\\frac{6}{7} = 0,\\left( {{\\rm{857142}}} \\right)\\]<\/td>\n<td>N\u00e3o<\/td>\n<td>\u00a0<\/td>\n<td>x<\/td>\n<\/tr>\n<tr>\n<td>B<\/td>\n<td>\\[ &#8211; \\frac{{17}}{6} = &#8211; \\frac{{17}}{{2 \\times 3}} = &#8211; {\\rm{2}}{\\rm{,8}}\\left( {\\rm{3}} \\right)\\]<\/td>\n<td>N\u00e3o<\/td>\n<td>\u00a0<\/td>\n<td>x<\/td>\n<\/tr>\n<tr>\n<td>C<\/td>\n<td>\\[ &#8211; \\frac{{15}}{9} = &#8211; \\frac{5}{3} = &#8211; {\\rm{1}}{\\rm{,}}\\left( {\\rm{6}} \\right)\\]<\/td>\n<td>N\u00e3o<\/td>\n<td>\u00a0<\/td>\n<td>x<\/td>\n<\/tr>\n<tr>\n<td>D<\/td>\n<td>\\[\\frac{7}{5} = \\frac{{14}}{{10}} = 1,4\\]<\/td>\n<td>Sim<\/td>\n<td>x<\/td>\n<td>\u00a0<\/td>\n<\/tr>\n<tr>\n<td>E<\/td>\n<td>\\[ &#8211; \\frac{{13}}{{52}} = &#8211; \\frac{1}{4} = &#8211; \\frac{{25}}{{100}} = &#8211; 0,25\\]<\/td>\n<td>Sim<\/td>\n<td>x<\/td>\n<td>\u00a0<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>\u00a0<\/p>\n<ol style=\"list-style-type: lower-alpha;\">\n<li>As fra\u00e7\u00f5es equivalentes a fra\u00e7\u00f5es decimais s\u00e3o apenas as fra\u00e7\u00f5es D e E, visto que, nas suas formas irredut\u00edveis, os seus denominadores n\u00e3o t\u00eam na sua decomposi\u00e7\u00e3o fatores primos diferentes de 2 e de 5.<br \/>Por isso, s\u00e3o apenas estas as fra\u00e7\u00f5es que se podem representar em d\u00edzima finita.<br \/><br \/><\/li>\n<li>A representa\u00e7\u00e3o em d\u00edzima de cada um dos n\u00fameros encontra-se registada na tabela acima.<br \/><br \/><\/li>\n<li>O n\u00famero A tem d\u00edzima infinita peri\u00f3dica de per\u00edodo \\({{\\rm{857142}}}\\)\u00a0e comprimento \\({\\rm{6}}\\).<br \/>O n\u00famero B tem d\u00edzima infinita peri\u00f3dica de per\u00edodo \\(3\\) e comprimento \\({\\rm{1}}\\).<br \/>O n\u00famero C tem d\u00edzima infinita peri\u00f3dica de per\u00edodo \\(6\\) e comprimento \\({\\rm{1}}\\).<\/li>\n<\/ol>\n<p>\u00a0<\/p>\n<p>\\[\\begin{array}{*{20}{c}}{6,}&amp;0&amp;0&amp;0&amp;0&amp;0&amp;0&amp;0&amp;0&amp;{}&amp;{}&amp;7&amp;{}&amp;{}&amp;{}&amp;{}&amp;{}&amp;{}&amp;{}\\\\\\hline{}&amp;4&amp;0&amp;{}&amp;{}&amp;{}&amp;{}&amp;{}&amp;{}&amp;{}&amp;{0,}&amp;8&amp;5&amp;7&amp;1&amp;4&amp;2&amp;8&amp;5\\\\{}&amp;{}&amp;5&amp;0&amp;{}&amp;{}&amp;{}&amp;{}&amp;{}&amp;{}&amp;{}&amp;{}&amp;{}&amp;{}&amp;{}&amp;{}&amp;{}&amp;{}&amp;{}\\\\{}&amp;{}&amp;{}&amp;1&amp;0&amp;{}&amp;{}&amp;{}&amp;{}&amp;{}&amp;{}&amp;{}&amp;{}&amp;{}&amp;{}&amp;{}&amp;{}&amp;{}&amp;{}\\\\{}&amp;{}&amp;{}&amp;{}&amp;3&amp;0&amp;{}&amp;{}&amp;{}&amp;{}&amp;{}&amp;{}&amp;{}&amp;{}&amp;{}&amp;{}&amp;{}&amp;{}&amp;{}\\\\{}&amp;{}&amp;{}&amp;{}&amp;{}&amp;2&amp;0&amp;{}&amp;{}&amp;{}&amp;{}&amp;{}&amp;{}&amp;{}&amp;{}&amp;{}&amp;{}&amp;{}&amp;{}\\\\{}&amp;{}&amp;{}&amp;{}&amp;{}&amp;{}&amp;6&amp;0&amp;{}&amp;{}&amp;{}&amp;{}&amp;{}&amp;{}&amp;{}&amp;{}&amp;{}&amp;{}&amp;{}\\\\{}&amp;{}&amp;{}&amp;{}&amp;{}&amp;{}&amp;{}&amp;4&amp;0&amp;{}&amp;{}&amp;{}&amp;{}&amp;{}&amp;{}&amp;{}&amp;{}&amp;{}&amp;{}\\\\{}&amp;{}&amp;{}&amp;{}&amp;{}&amp;{}&amp;{}&amp;{}&amp;5&amp;{}&amp;{}&amp;{}&amp;{}&amp;{}&amp;{}&amp;{}&amp;{}&amp;{}&amp;{}\\end{array}\\]<\/p>\n<p>\u00a0<\/p>\n<p>\\[\\begin{array}{*{20}{c}}1&amp;{7,}&amp;0&amp;0&amp;0&amp;{}&amp;6&amp;{}&amp;{}&amp;{}\\\\\\hline{}&amp;5&amp;0&amp;{}&amp;{}&amp;{}&amp;{2,}&amp;8&amp;3&amp;3\\\\{}&amp;{}&amp;2&amp;0&amp;{}&amp;{}&amp;{}&amp;{}&amp;{}&amp;{}\\\\{}&amp;{}&amp;{}&amp;2&amp;0&amp;{}&amp;{}&amp;{}&amp;{}&amp;{}\\\\{}&amp;{}&amp;{}&amp;{}&amp;2&amp;{}&amp;{}&amp;{}&amp;{}&amp;{}\\end{array}\\]<\/p>\n<p>\u00a0<\/p>\n<p>\\[\\begin{array}{*{20}{c}}{5,}&amp;0&amp;0&amp;{}&amp;3&amp;{}&amp;{}\\\\\\hline2&amp;0&amp;{}&amp;{}&amp;{1,}&amp;6&amp;6\\\\{}&amp;2&amp;0&amp;{}&amp;{}&amp;{}&amp;{}\\\\{}&amp;{}&amp;2&amp;{}&amp;{}&amp;{}&amp;{}\\end{array}\\]<\/p>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_22428' onClick='GTTabs_show(0,22428)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Considera os n\u00fameros seguintes: \\[\\begin{array}{*{20}{l}}{\\frac{6}{7}}&amp;{ &#8211; \\frac{{17}}{6}}&amp;{ &#8211; \\frac{{15}}{9}}&amp;{\\frac{7}{5}}&amp;{ &#8211; \\frac{{13}}{{52}}}\\end{array}\\] Indica as fra\u00e7\u00f5es que se podem representar em d\u00edzima finita, identificando as fra\u00e7\u00f5es equivalentes a fra\u00e7\u00f5es decimais. Escreve essas fra\u00e7\u00f5es&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":14057,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[100,97,664],"tags":[424,261,665,666],"series":[],"class_list":["post-22428","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-8--ano","category-aplicando","category-numeros-reais","tag-8-o-ano","tag-dizima","tag-dizima-finita","tag-dizima-infinita-periodica"],"views":230,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/Mat02.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/22428","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=22428"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/22428\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/14057"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=22428"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=22428"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=22428"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=22428"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}