\n| \\[ – \\frac{3}{5}\\]<\/td>\n | \\[\\frac{1}{3}\\]<\/td>\n | \\[ – \\frac{{45}}{{11}}\\]<\/td>\n | \\[\\frac{{34}}{{27}}\\]<\/td>\n | \\[\\frac{{13}}{8}\\]<\/td>\n | \\[\\frac{7}{{1250}}\\]<\/td>\n | \\[ – \\frac{{13}}{{36}}\\]<\/td>\n | \\[\\frac{1}{2}\\]<\/td>\n | \\[\\frac{{23}}{{220}}\\]<\/td>\n | \\[ – \\frac{8}{{10}}\\]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n \u00a0<\/p>\n Come\u00e7\u00e1mos por decompor os denominadores das fra\u00e7\u00f5es em fatores primos e, no caso de existir, determin\u00e1mos seguidamente uma fra\u00e7\u00e3o decimal equivalente e a respetiva d\u00edzima.<\/p>\n Depois, utilizando o algoritmo da divis\u00e3o (apresentado abaixo), procedeu-se \u00e0 obten\u00e7\u00e3o da representa\u00e7\u00e3o em d\u00edzima das fra\u00e7\u00f5es n\u00e3o decimais, que tamb\u00e9m se registou na tabela imediatamente a seguir.<\/p>\n \u00a0<\/p>\n \n\n\n| A<\/span><\/td>\n | \\[ – \\frac{3}{5} = – \\frac{3}{5} \\times \\frac{2}{2} = – \\frac{6}{{10}} = – 0,6\\]<\/span><\/td>\n | F<\/span><\/td>\n | \\[\\frac{7}{{1250}} = \\frac{7}{{2 \\times 5 \\times 5 \\times 5 \\times 5}} \\times \\frac{{2 \\times 2 \\times 2}}{{2 \\times 2 \\times 2}} = \\frac{{56}}{{10000}} = 0,0056\\]<\/span><\/td>\n<\/tr>\n\n| B<\/span><\/td>\n | \\[\\frac{1}{3} = 0,\\left( 3 \\right)\\]<\/span><\/td>\n | G<\/span><\/td>\n | \\[ – \\frac{{13}}{{36}} = – \\frac{{13}}{{2 \\times 2 \\times 3 \\times 3}} = – 0,36\\left( 1 \\right)\\]<\/span><\/td>\n<\/tr>\n\n| C<\/span><\/td>\n | \\[ – \\frac{{45}}{{11}} = – 4,\\left( {09} \\right)\\]<\/span><\/td>\n | H<\/span><\/td>\n | \\[\\frac{1}{2} = \\frac{1}{2} \\times \\frac{5}{5} = \\frac{5}{{10}} = 0,5\\]<\/span><\/td>\n<\/tr>\n\n| D<\/span><\/td>\n | \\[\\frac{{34}}{{27}} = \\frac{{34}}{{3 \\times 3 \\times 3}} = 1,\\left( {259} \\right)\\]<\/span><\/td>\n | I<\/span><\/td>\n | \\[\\frac{{23}}{{220}} = \\frac{{23}}{{2 \\times 2 \\times 5 \\times 11}} = 0,10\\left( {45} \\right)\\]<\/span><\/td>\n<\/tr>\n\n| E<\/span><\/td>\n | \\[\\frac{{13}}{8} = \\frac{{13}}{{2 \\times 2 \\times 2}} \\times \\frac{{5 \\times 5 \\times 5}}{{5 \\times 5 \\times 5}} = \\frac{{1625}}{{1000}} = 1,625\\]<\/span><\/td>\n | J<\/span><\/td>\n | \\[ – \\frac{8}{{10}} = – 0,8\\]<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n \u00a0<\/p>\n \n- S\u00e3o equivalentes a fra\u00e7\u00f5es decimais as seguintes fra\u00e7\u00f5es: A<\/span>, E<\/span>, F<\/span>, H<\/span> e J<\/span>.
As respetivas fra\u00e7\u00f5es decimais est\u00e3o escritas na tabela acima.
<\/li>\n- As respetivas d\u00edzimas das fra\u00e7\u00f5es equivalentes a fra\u00e7\u00f5es decimais est\u00e3o registadas na tabela acima.
<\/li>\n - As fra\u00e7\u00f5es decimais<\/strong> podem ser representadas sob a forma de d\u00edzimas finitas<\/strong>.
<\/li>\n- Os algoritmos est\u00e3o apresentados abaixo e as d\u00edzimas das fra\u00e7\u00f5es n\u00e3o equivalentes a fra\u00e7\u00f5es decimais (B<\/span>, C<\/span>. D<\/span>, G<\/span> e I<\/span>) est\u00e3o registadas na tabela acima.
<\/li>\n- As fra\u00e7\u00f5es que n\u00e3o s\u00e3o equivalentes a fra\u00e7\u00f5es decimais<\/strong> podem ser representadas sob a forma de d\u00edzimas infinitas peri\u00f3dicas<\/strong>.<\/li>\n<\/ol>\n
\u00a0<\/p>\n Aplica\u00e7\u00e3o do algoritmo da divis\u00e3o:<\/h6>\n\u00a0<\/p>\n \n\n\n| B<\/span><\/td>\n | \\[\\frac{1}{3} = 0,\\left( 3 \\right)\\]<\/span><\/td>\n | \\[\\begin{array}{*{20}{c}}{1,}&0&0&{}&{}&3&{}\\\\\\hline{}&1&0&{}&{0,}&3&3\\\\{}&{}&1&{}&{}&{}&{}\\end{array}\\]<\/td>\n<\/tr>\n | \n| C<\/span><\/td>\n | \\[ – \\frac{{45}}{{11}} = – 4,\\left( {09} \\right)\\]<\/span><\/td>\n | \\[\\begin{array}{*{20}{c}}4&{5,}&0&0&0&{}&1&1&{}&{}\\\\\\hline{}&1&0&0&{}&{}&{4,}&0&9&0\\\\{}&{}&0&1&0&{}&{}&{}&{}&{}\\end{array}\\]<\/td>\n<\/tr>\n | \n| D<\/span><\/td>\n | \\[\\frac{{34}}{{27}} = \\frac{{34}}{{3 \\times 3 \\times 3}} = 1,\\left( {259} \\right)\\]<\/span><\/td>\n | \\[\\begin{array}{*{20}{c}}3&{4,}&0&0&0&0&{}&2&7&{}&{}&{}\\\\\\hline{}&7&0&{}&{}&{}&{}&{1,}&2&5&9&2\\\\{}&1&6&0&{}&{}&{}&{}&{}&{}&{}&{}\\\\{}&{}&2&5&0&{}&{}&{}&{}&{}&{}&{}\\\\{}&{}&{}&0&7&0&{}&{}&{}&{}&{}&{}\\\\{}&{}&{}&{}&1&6&{}&{}&{}&{}&{}&{}\\end{array}\\]<\/td>\n<\/tr>\n | \n| G<\/span><\/td>\n | \\[ – \\frac{{13}}{{36}} = – \\frac{{13}}{{2 \\times 2 \\times 3 \\times 3}} = – 0,36\\left( 1 \\right)\\]<\/span><\/td>\n | \\[\\begin{array}{*{20}{c}}1&{3,}&0&0&0&0&{}&{}&3&6&{}&{}\\\\\\hline{}&2&2&0&{}&{}&{}&{0,}&3&6&1&1\\\\{}&{}&0&4&0&{}&{}&{}&{}&{}&{}&{}\\\\{}&{}&{}&{}&4&0&{}&{}&{}&{}&{}&{}\\\\{}&{}&{}&{}&{}&4&{}&{}&{}&{}&{}&{}\\end{array}\\]<\/td>\n<\/tr>\n | \n| I<\/span><\/td>\n | \\[\\frac{{23}}{{220}} = \\frac{{23}}{{2 \\times 2 \\times 5 \\times 11}} = 0,10\\left( {45} \\right)\\]<\/span><\/td>\n | \\[\\begin{array}{*{20}{c}}2&{3,}&0&0&0&0&0&{}&{}&2&2&0&{}&{}\\\\\\hline{}&1&0&0&0&{}&{}&{}&{0,}&1&0&4&5&4\\\\{}&{}&1&2&0&0&{}&{}&{}&{}&{}&{}&{}&{}\\\\{}&{}&{}&1&0&0&0&{}&{}&{}&{}&{}&{}&{}\\\\{}&{}&{}&{}&1&2&0&{}&{}&{}&{}&{}&{}&{}\\end{array}\\]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n \u00a0<\/p>\n << Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"Enunciado Resolu\u00e7\u00e3o Enunciado Os n\u00fameros racionais podem ser representados na forma de fra\u00e7\u00e3o ou na forma de d\u00edzima.Considera os seguintes n\u00fameros racionais: A B C D E F G H I J \\[ –...<\/p>\n","protected":false},"author":1,"featured_media":22367,"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-22342","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":366,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/10\/Mat268.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/22342","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=22342"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/22342\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/22367"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=22342"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=22342"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=22342"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=22342"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}} | | | | | | |