{"id":205,"date":"2023-06-24T04:56:26","date_gmt":"2023-06-24T04:56:26","guid":{"rendered":"https:\/\/physigeek.com\/pt\/aproximacao-de-numeros-matematicos\/"},"modified":"2023-06-24T04:56:26","modified_gmt":"2023-06-24T04:56:26","slug":"aproximacao-de-numeros-matematicos","status":"publish","type":"post","link":"https:\/\/physigeek.com\/pt\/aproximacao-de-numeros-matematicos\/","title":{"rendered":"Aproxima\u00e7\u00e3o de n\u00fameros (matem\u00e1tica)"},"content":{"rendered":"<p>Este artigo explica o que \u00e9 aproxima\u00e7\u00e3o num\u00e9rica e como ela \u00e9 feita. Assim, voc\u00ea encontrar\u00e1 os diferentes tipos de aproxima\u00e7\u00e3o existentes, bem como v\u00e1rios exemplos de cada um. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%C2%BFQue-es-la-aproximacion-de-numeros\"><\/span> O que \u00e9 aproxima\u00e7\u00e3o num\u00e9rica?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Em matem\u00e1tica, <strong>aproxima\u00e7\u00e3o<\/strong> \u00e9 um processo no qual um n\u00famero \u00e9 transformado em outro muito pr\u00f3ximo. Em outras palavras, <strong>aproximar um n\u00famero<\/strong> envolve alterar seu valor e arredond\u00e1-lo para um n\u00famero muito pr\u00f3ximo.<\/p>\n<p> Geralmente, o s\u00edmbolo \u2248 \u00e9 usado para representar a aproxima\u00e7\u00e3o de um n\u00famero, embora os s\u00edmbolos ~ ou =~ tamb\u00e9m possam ser usados, mas s\u00e3o mais informais.<\/p>\n<p> O valor aproximado \u00e9, portanto, o n\u00famero cujo valor verdadeiro \u00e9 fechado. E a diferen\u00e7a entre os dois \u00e9 o erro de aproxima\u00e7\u00e3o. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Aproximacion-de-numeros-naturales\"><\/span> Aproxima\u00e7\u00e3o de n\u00fameros naturais<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> A <strong>aproxima\u00e7\u00e3o dos n\u00fameros naturais<\/strong> consiste em aumentar em 1 ou manter o mesmo n\u00famero que queremos aproximar, e os demais n\u00fameros da direita tornam-se 0.<\/p>\n<ul style=\"color:#4fd12f; font-weight: bold;\">\n<li style=\"margin-bottom:15px\"> <span style=\"color:#101010;font-weight: normal;\">Se o d\u00edgito seguinte ao \u00faltimo d\u00edgito significativo for maior ou igual a 5, o \u00faltimo d\u00edgito significativo \u00e9 aumentado em 1 ( <strong>arredondado<\/strong> ).<\/span><\/li>\n<li> <span style=\"color:#101010;font-weight: normal;\">Se o d\u00edgito seguinte ao \u00faltimo d\u00edgito significativo for menor que 5, o \u00faltimo d\u00edgito significativo n\u00e3o ser\u00e1 alterado ( <strong>arredondado para baixo ou para baixo<\/strong> ).<\/span><\/li>\n<\/ul>\n<p> Por exemplo, quando arredondamos as centenas para o n\u00famero 1574, obtemos o n\u00famero 1600, pois o n\u00famero depois das centenas (7) \u00e9 maior que 5.<\/p>\n<p class=\"has-text-align-center\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-1532ea74f55a77d4cb72b51a19d69dbd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\" 1574 \\quad \\color{orange}\\bm{\\longrightarrow}\\quad\\color{noir} 1600\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"223\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p> No entanto, a aproxima\u00e7\u00e3o das dezenas do n\u00famero 891 permanece em 890, uma vez que o d\u00edgito que vem depois das dezenas \u00e9 o d\u00edgito 1 e, portanto, \u00e9 menor que 5.<\/p>\n<p class=\"has-text-align-center\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-d6e9f7a68f045e534fd30f56bf306bd4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\" 891 \\quad \\color{orange}\\bm{\\longrightarrow}\\quad\\color{noir} 890\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"206\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p> Abaixo voc\u00ea pode ver mais <strong>exemplos de aproxima\u00e7\u00f5es de n\u00fameros naturais<\/strong> :<\/p>\n<ol style=\"color:#4fd12f; font-weight: bold;\">\n<li style=\"margin-bottom:12px\"> <span style=\"color:#101010;font-weight: normal;\">Aproxima\u00e7\u00e3o para dezenas de 1352 <span style=\"color:#4fd12f\"><strong>\u2192<\/strong><\/span> 1350<\/span><\/li>\n<li style=\"margin-bottom:12px\"> <span style=\"color:#101010;font-weight: normal;\">Aproxima\u00e7\u00e3o para centenas de 45851 <span style=\"color:#4fd12f\"><strong>\u2192<\/strong><\/span> 45900<\/span><\/li>\n<li> <span style=\"color:#101010;font-weight: normal;\">Aproxima\u00e7\u00e3o de milhares de 923802 <span style=\"color:#4fd12f\"><strong>\u2192<\/strong><\/span> 924000.<\/span> <\/li>\n<\/ol>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Aproximacion-de-numeros-decimales\"><\/span> Aproxima\u00e7\u00e3o de n\u00fameros decimais<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Existem dois m\u00e9todos diferentes para <strong>aproximar n\u00fameros decimais<\/strong> :<\/p>\n<ul style=\"color:#4fd12f; font-weight: bold;\">\n<li style=\"margin-bottom:15px\"> <span style=\"color:#101010;font-weight: normal;\"><strong>Arredondamento<\/strong> : dependendo do caso, a \u00faltima casa decimal significativa \u00e9 aumentada de 1 ou mantida inalterada.<\/span><\/li>\n<li> <span style=\"color:#101010;font-weight: normal;\"><strong>Truncamento<\/strong> : A \u00faltima casa decimal significativa permanece sempre a mesma.<\/span><\/li>\n<\/ul>\n<p> Cada tipo de abordagem \u00e9 explicado em detalhes abaixo.<\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Redondeo\"><\/span> Redondo<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p> No <strong>arredondamento,<\/strong> todas as casas decimais ap\u00f3s a \u00faltima casa decimal significativa s\u00e3o eliminadas e, adicionalmente, a casa decimal para a qual se deseja arredondar \u00e9 aumentada em 1 ou mantida igual, conforme o caso:<\/p>\n<ul style=\"color:#4fd12f; font-weight: bold;\">\n<li style=\"margin-bottom:15px\"> <span style=\"color:#101010;font-weight: normal;\">Se a casa decimal seguinte \u00e0 \u00faltima casa decimal for maior ou igual a 5, a \u00faltima casa decimal \u00e9 aumentada de 1 ( <strong>arredondado<\/strong> ).<\/span><\/li>\n<li style=\"margin-bottom:15px\"> <span style=\"color:#101010;font-weight: normal;\">Se a casa decimal ap\u00f3s a \u00faltima casa decimal for menor que 5, a \u00faltima casa decimal permanece a mesma ( <strong>arredondada para cima ou para baixo<\/strong> ).<\/span><\/li>\n<\/ul>\n<p> Por exemplo, o n\u00famero decimal 3,14159265 arredondado para o d\u00e9cimo mais pr\u00f3ximo \u00e9 3,1 porque o pr\u00f3ximo n\u00famero decimal (4) \u00e9 menor que 5.<\/p>\n<p class=\"has-text-align-center\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-cb8fd7a4232dad6a3bc1e0c62b307b48_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\" 3.14159265 \\quad \\color{orange}\\bm{\\longrightarrow}\\quad\\color{noir} 3.1\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"259\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p> Por outro lado, se arredondarmos o n\u00famero decimal 52,84917 para o cent\u00e9simo mais pr\u00f3ximo, obtemos 52,85, pois o pr\u00f3ximo d\u00edgito decimal (9) \u00e9 maior que 5.<\/p>\n<p class=\"has-text-align-center\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-726107f137233116828d1f13f68c5dd1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\" 52,84917 \\quad \\color{orange}\\bm{\\longrightarrow}\\quad\\color{noir} 52,85\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"265\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p> Outros <strong>exemplos de arredondamento de n\u00fameros decimais<\/strong> s\u00e3o mostrados abaixo:<\/p>\n<ol style=\"color:#4fd12f; font-weight: bold;\">\n<li style=\"margin-bottom:12px\"> <span style=\"color:#101010;font-weight: normal;\">Arredondado para o d\u00e9cimo mais pr\u00f3ximo de 445,945 <span style=\"color:#4fd12f\"><strong>\u2192<\/strong><\/span> 445,9<\/span><\/li>\n<li style=\"margin-bottom:12px\"> <span style=\"color:#101010;font-weight: normal;\">Arredondado para o cent\u00e9simo mais pr\u00f3ximo de 7,03522 <span style=\"color:#4fd12f\"><strong>\u2192<\/strong><\/span> 7,04<\/span><\/li>\n<li> <span style=\"color:#101010;font-weight: normal;\">Arredondado para o mil\u00e9simo mais pr\u00f3ximo de 39,802719 <span style=\"color:#4fd12f\"><strong>\u2192<\/strong><\/span> 39,803<\/span><\/li>\n<\/ol>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Truncamiento\"><\/span>Truncamento<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p> <strong>O truncamento<\/strong> reduz o n\u00famero de casas decimais, eliminando aquelas que s\u00e3o menos significativas. Em outras palavras, o truncamento consiste em deletar os d\u00edgitos \u00e0 direita do d\u00edgito pelo qual se deseja truncar.<\/p>\n<p> Por exemplo, quando aproximamos o n\u00famero 65,71834 truncando em cent\u00e9simos, obtemos o n\u00famero 65,71, pois simplesmente retiramos as casas decimais ap\u00f3s os cent\u00e9simos (834).<\/p>\n<p class=\"has-text-align-center\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-fa5a9534b3756e3e86f62f3e4c281cf0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\" 65,71834 \\quad \\color{orange}\\bm{\\longrightarrow}\\quad\\color{noir} 65,71\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"265\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p> Assim, ao truncar um n\u00famero, n\u00e3o importa se ap\u00f3s a \u00faltima casa decimal significativa existe um n\u00famero maior, igual ou menor que 5, pois todas as casas decimais subsequentes devem sempre ser eliminadas.<\/p>\n<p> Se voc\u00ea olhar o \u00faltimo exemplo, se tiv\u00e9ssemos arredondado o n\u00famero 65,71834 ter\u00edamos obtido 65,72. No entanto, usando truncamento obtemos 65,71. Concluindo, o n\u00famero aproximado pode ser diferente dependendo do m\u00e9todo de aproxima\u00e7\u00e3o escolhido.<\/p>\n<p> Abaixo voc\u00ea pode ver mais <strong>exemplos de aproxima\u00e7\u00e3o de truncamento<\/strong> :<\/p>\n<ol style=\"color:#4fd12f; font-weight: bold;\">\n<li style=\"margin-bottom:12px\"> <span style=\"color:#101010;font-weight: normal;\">Truncamento por unidade 9 634 <strong><span style=\"color:#4fd12f\">\u2192<\/span><\/strong> 9<\/span><\/li>\n<li style=\"margin-bottom:12px\"> <span style=\"color:#101010;font-weight: normal;\">Truncamento pelo d\u00e9cimo de 4,13558 <strong><span style=\"color:#4fd12f\">\u2192<\/span><\/strong> 4,1<\/span><\/li>\n<li style=\"margin-bottom:12px\"> <span style=\"color:#101010;font-weight: normal;\">Truncamento ao cent\u00e9simo de 71,0442 <strong><span style=\"color:#4fd12f\">\u2192<\/span><\/strong> 71,04<\/span><\/li>\n<\/ol>\n","protected":false},"excerpt":{"rendered":"<p>Este artigo explica o que \u00e9 aproxima\u00e7\u00e3o num\u00e9rica e como ela \u00e9 feita. Assim, voc\u00ea encontrar\u00e1 os diferentes tipos de aproxima\u00e7\u00e3o existentes, bem como v\u00e1rios exemplos de cada um. O que \u00e9 aproxima\u00e7\u00e3o num\u00e9rica? Em matem\u00e1tica, aproxima\u00e7\u00e3o \u00e9 um processo no qual um n\u00famero \u00e9 transformado em outro muito pr\u00f3ximo. Em outras palavras, aproximar um &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/physigeek.com\/pt\/aproximacao-de-numeros-matematicos\/\"> <span class=\"screen-reader-text\">Aproxima\u00e7\u00e3o de n\u00fameros (matem\u00e1tica)<\/span> Leia mais &raquo;<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"","footnotes":""},"categories":[18],"tags":[],"class_list":["post-205","post","type-post","status-publish","format-standard","hentry","category-numeros"],"yoast_head":"<!-- This site is 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