{"id":22585,"date":"2022-10-21T22:41:58","date_gmt":"2022-10-21T21:41:58","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=22585"},"modified":"2022-10-22T01:30:35","modified_gmt":"2022-10-22T00:30:35","slug":"escreve-sob-a-forma-de-dizima","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=22585","title":{"rendered":"Escreve sob a forma de d\u00edzima"},"content":{"rendered":"\n<p><ul id='GTTabs_ul_22585' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_22585' class='GTTabs_curr'><a  id=\"22585_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_22585' ><a  id=\"22585_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_22585'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>Escreve sob a forma de d\u00edzima finita, atrav\u00e9s da fra\u00e7\u00e3o decimal, ou sob a forma de d\u00edzima infinita peri\u00f3dica, utilizando o algoritmo da divis\u00e3o, os seguintes n\u00fameros, identificando o per\u00edodo e o comprimento do per\u00edodo das d\u00edzimas infinitas.<\/p>\n<table style=\"border-collapse: collapse;\">\n<tbody>\n<tr>\n<td>\\[\\frac{3}{8}\\]<\/td>\n<td>\\[ &#8211; \\frac{8}{3}\\]<\/td>\n<td>\\[\\frac{{13}}{5}\\]<\/td>\n<td>\\[ &#8211; \\frac{{13}}{8}\\]<\/td>\n<\/tr>\n<tr>\n<td>\\[\\frac{{12}}{7}\\]<\/td>\n<td>\\[\\frac{{128}}{{72}}\\]<\/td>\n<td>\\[\\frac{{13}}{{80}}\\]<\/td>\n<td>\\[\\frac{{72}}{{25}}\\]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_22585' onClick='GTTabs_show(1,22585)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_22585'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<p>A aplica\u00e7\u00e3o do algoritmo da divis\u00e3o est\u00e1 no final da p\u00e1gina.<\/p>\n<table style=\"border-collapse: collapse;\">\n<tbody>\n<tr>\n<td>\u00a0<\/td>\n<td>\u00a0<\/td>\n<td>\u00a0 D\u00edzima finita\u00a0<\/td>\n<td>D\u00edzima infinita peri\u00f3dica<\/td>\n<td>Per\u00edodo<\/td>\n<td>Comprimento do per\u00edodo<\/td>\n<\/tr>\n<tr>\n<td>A<\/td>\n<td>\\[\\frac{3}{8} = \\frac{3}{{{2^3}}} \\times \\frac{{{5^3}}}{{{5^3}}} = \\frac{{375}}{{1000}} = 0,375\\]<\/td>\n<td>x<\/td>\n<td>\u00a0<\/td>\n<td>\u00a0<\/td>\n<td>\u00a0<\/td>\n<\/tr>\n<tr>\n<td>B<\/td>\n<td>\\[ &#8211; \\frac{8}{3} = &#8211; 2,\\left( 6 \\right)\\]<\/td>\n<td>\u00a0<\/td>\n<td>x<\/td>\n<td>\\[6\\]<\/td>\n<td>\\[1\\]<\/td>\n<\/tr>\n<tr>\n<td>C<\/td>\n<td>\\[\\frac{{13}}{5} = \\frac{{13}}{5} \\times \\frac{2}{2} = \\frac{{26}}{{10}} = 2,6\\]<\/td>\n<td>x<\/td>\n<td>\u00a0<\/td>\n<td>\u00a0<\/td>\n<td>\u00a0<\/td>\n<\/tr>\n<tr>\n<td>D<\/td>\n<td>\\[ &#8211; \\frac{{13}}{8} = &#8211; \\frac{{13}}{{{2^3}}} \\times \\frac{{{5^3}}}{{{5^3}}} = &#8211; \\frac{{1625}}{{1000}} = &#8211; 1,625\\]<\/td>\n<td>x<\/td>\n<td>\u00a0<\/td>\n<td>\u00a0<\/td>\n<td>\u00a0<\/td>\n<\/tr>\n<tr>\n<td>E<\/td>\n<td>\\[\\frac{{12}}{7} = {\\rm{1}}{\\rm{,}}\\left( {{\\rm{714285}}} \\right)\\]<\/td>\n<td>\u00a0<\/td>\n<td>x<\/td>\n<td>\\[{{\\rm{714285}}}\\]<\/td>\n<td>\u00a0\\[6\\]<\/td>\n<\/tr>\n<tr>\n<td>F<\/td>\n<td>\\[\\frac{{128}}{{72}} = \\frac{{{2^7}}}{{{2^3} \\times {3^2}}} = \\frac{{{2^4}}}{{{3^2}}} = \\frac{{16}}{9} = 1,\\left( 7 \\right)\\]<\/td>\n<td>\u00a0<\/td>\n<td>x<\/td>\n<td>\\[7\\]<\/td>\n<td>\\[1\\]<\/td>\n<\/tr>\n<tr>\n<td>G<\/td>\n<td>\\[\\frac{{13}}{{80}} = \\frac{{13}}{{{2^4} \\times 5}} \\times \\frac{{{5^3}}}{{{5^3}}} = \\frac{{1625}}{{10000}} = 0,1625\\]<\/td>\n<td>x<\/td>\n<td>\u00a0<\/td>\n<td>\u00a0<\/td>\n<td>\u00a0<\/td>\n<\/tr>\n<tr>\n<td>H<\/td>\n<td>\\[\\frac{{72}}{{25}} = \\frac{{72}}{{25}} \\times \\frac{4}{4} = \\frac{{288}}{{100}} = 2,88\\]<\/td>\n<td>x<\/td>\n<td>\u00a0<\/td>\n<td>\u00a0<\/td>\n<td>\u00a0<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>\u00a0<\/p>\n<p>\\[\\begin{array}{*{20}{c}}{8,}&amp;0&amp;0&amp;{}&amp;3&amp;{}&amp;{}\\\\\\hline2&amp;0&amp;{}&amp;{}&amp;{2,}&amp;6&amp;6\\\\{}&amp;2&amp;0&amp;{}&amp;{}&amp;{}&amp;{}\\\\{}&amp;{}&amp;2&amp;{}&amp;{}&amp;{}&amp;{}\\end{array}\\]<\/p>\n<p>\u00a0<\/p>\n<p>\\[\\begin{array}{*{20}{c}}1&amp;{6,}&amp;0&amp;0&amp;{}&amp;9&amp;{}&amp;{}\\\\\\hline{}&amp;7&amp;0&amp;{}&amp;{}&amp;{1,}&amp;7&amp;7\\\\{}&amp;{}&amp;7&amp;0&amp;{}&amp;{}&amp;{}&amp;{}\\\\{}&amp;{}&amp;{}&amp;7&amp;{}&amp;{}&amp;{}&amp;{}\\end{array}\\]<\/p>\n<p>\u00a0<\/p>\n<p>\\[\\begin{array}{*{20}{c}}1&amp;{2,}&amp;0&amp;0&amp;0&amp;0&amp;0&amp;0&amp;0&amp;0&amp;{}&amp;7&amp;{}&amp;{}&amp;{}&amp;{}&amp;{}&amp;{}&amp;{}&amp;{}\\\\\\hline{}&amp;5&amp;0&amp;{}&amp;{}&amp;{}&amp;{}&amp;{}&amp;{}&amp;{}&amp;{}&amp;{1,}&amp;7&amp;1&amp;4&amp;2&amp;8&amp;5&amp;7&amp;1\\\\{}&amp;{}&amp;1&amp;0&amp;{}&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;{}&amp;2&amp;0&amp;{}&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;{}&amp;4&amp;0&amp;{}&amp;{}&amp;{}&amp;{}&amp;{}&amp;{}&amp;{}&amp;{}&amp;{}&amp;{}&amp;{}&amp;{}\\\\{}&amp;{}&amp;{}&amp;{}&amp;{}&amp;{}&amp;{}&amp;5&amp;0&amp;{}&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;{}&amp;3&amp;{}&amp;{}&amp;{}&amp;{}&amp;{}&amp;{}&amp;{}&amp;{}&amp;{}&amp;{}\\end{array}\\]<\/p>\n<p>\u00a0<\/p>\n<p>\u00a0<\/p>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_22585' onClick='GTTabs_show(0,22585)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Escreve sob a forma de d\u00edzima finita, atrav\u00e9s da fra\u00e7\u00e3o decimal, ou sob a forma de d\u00edzima infinita peri\u00f3dica, utilizando o algoritmo da divis\u00e3o, os seguintes n\u00fameros, identificando o per\u00edodo e&#46;&#46;&#46;<\/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":[100,97,664],"tags":[424,665,666,668],"series":[],"class_list":["post-22585","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-finita","tag-dizima-infinita-periodica","tag-dizimas"],"views":292,"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\/22585","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=22585"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/22585\/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=22585"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=22585"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=22585"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=22585"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}