{"id":341576,"date":"2025-04-09T11:22:55","date_gmt":"2025-04-09T18:22:55","guid":{"rendered":"https:\/\/barrazacarlos.com\/diferencias-entre-numeros-racionales-e-irracionales\/"},"modified":"2025-08-11T23:05:54","modified_gmt":"2025-08-12T06:05:54","slug":"diferencias-entre-numeros-racionales-e-irracionales","status":"publish","type":"post","link":"https:\/\/barrazacarlos.com\/es\/diferencias-entre-numeros-racionales-e-irracionales\/","title":{"rendered":"Diferencias entre n\u00fameros racionales e irracionales"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-post\" data-elementor-id=\"341576\" class=\"elementor elementor-341576 elementor-341553\" data-elementor-post-type=\"post\">\n\t\t\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-6186b235 elementor-section-height-min-height elementor-section-content-bottom elementor-section-boxed elementor-section-height-default elementor-section-items-middle\" data-id=\"6186b235\" data-element_type=\"section\" data-e-type=\"section\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;}\">\n\t\t\t\t\t\t\t<div class=\"elementor-background-overlay\"><\/div>\n\t\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-wider\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-23979a25\" data-id=\"23979a25\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<section class=\"elementor-section elementor-inner-section elementor-element elementor-element-2a5d3139 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"2a5d3139\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-50 elementor-inner-column elementor-element elementor-element-67389c7a\" data-id=\"67389c7a\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-13a16967 elementor-widget elementor-widget-heading\" data-id=\"13a16967\" data-element_type=\"widget\" data-e-type=\"widget\" data-settings=\"{&quot;_animation&quot;:&quot;none&quot;,&quot;_animation_delay&quot;:&quot;800&quot;}\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h1 class=\"elementor-heading-title elementor-size-default\">Diferencias entre n\u00fameros racionales e irracionales<\/h1>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-61e6108b elementor-widget elementor-widget-text-editor\" data-id=\"61e6108b\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p class=\"\" data-start=\"57\" data-end=\"444\">El <strong data-start=\"61\" data-end=\"78\">sistema num\u00e9rico<\/strong> es vasto y rico, y consta de distintas categor\u00edas que definen la naturaleza de los valores que utilizamos en matem\u00e1ticas y en la vida real. Entre ellos, <strong data-start=\"214\" data-end=\"249\">los n\u00fameros racionales e irracionales<\/strong> son clasificaciones fundamentales bajo el paraguas de los <strong data-start=\"304\" data-end=\"320\">n\u00fameros reales<\/strong>. Aunque ambos son <strong data-start=\"340\" data-end=\"356\">n\u00fameros reales<\/strong>, difieren significativamente en cuanto a sus propiedades, representaciones y comportamiento.  <\/p><p class=\"\" data-start=\"446\" data-end=\"698\">Comprender la <strong data-start=\"464\" data-end=\"510\">diferencia entre<\/strong> n\u00fameros <strong data-start=\"464\" data-end=\"510\">racionales e irracionales<\/strong> es esencial para estudiantes, educadores y cualquier persona interesada en la estructura de las matem\u00e1ticas. A continuaci\u00f3n se detallan siete diferencias que definen estos dos importantes tipos de n\u00fameros. <\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-50 elementor-inner-column elementor-element elementor-element-69c12ede\" data-id=\"69c12ede\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-22e21fe0 elementor-widget elementor-widget-image\" data-id=\"22e21fe0\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<img fetchpriority=\"high\" decoding=\"async\" width=\"1280\" height=\"720\" src=\"https:\/\/barrazacarlos.com\/wp-content\/uploads\/2025\/04\/Differences-Between-Rational-and-Irrational-Numbers.webp\" class=\"attachment-full size-full 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elementor-widget-heading\" data-id=\"6400cefd\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<span class=\"elementor-heading-title elementor-size-default\">Escrito por<\/span>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-4e2e4233 elementor-align-left elementor-widget elementor-widget-post-info\" data-id=\"4e2e4233\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"post-info.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<ul class=\"elementor-inline-items elementor-icon-list-items elementor-post-info\">\n\t\t\t\t\t\t\t\t<li class=\"elementor-icon-list-item elementor-repeater-item-ef43aea elementor-inline-item\" itemprop=\"author\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-icon-list-text elementor-post-info__item 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href=\"https:\/\/barrazacarlos.com\/es\/category\/desarrollo-profesional\/\" class=\"elementor-post-info__terms-list-item\">Desarrollo Profesional<\/a>\t\t\t\t<\/span>\n\t\t\t\t\t<\/span>\n\t\t\t\t\t\t\t\t<\/li>\n\t\t\t\t<\/ul>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-56f4521b elementor-toc--minimized-on-tablet elementor-widget elementor-widget-table-of-contents\" data-id=\"56f4521b\" data-element_type=\"widget\" data-e-type=\"widget\" data-settings=\"{&quot;headings_by_tags&quot;:[&quot;h2&quot;],&quot;exclude_headings_by_selector&quot;:[],&quot;collapse_subitems&quot;:&quot;yes&quot;,&quot;no_headings_message&quot;:&quot;No headings were found on this 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la tabla de contenidos\"><svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" viewBox=\"0 0 448 512\"><path d=\"M207.029 381.476L12.686 187.132c-9.373-9.373-9.373-24.569 0-33.941l22.667-22.667c9.357-9.357 24.522-9.375 33.901-.04L224 284.505l154.745-154.021c9.379-9.335 24.544-9.317 33.901.04l22.667 22.667c9.373 9.373 9.373 24.569 0 33.941L240.971 381.476c-9.373 9.372-24.569 9.372-33.942 0z\"><\/path><\/svg><\/div>\n\t\t\t\t<div class=\"elementor-toc__toggle-button elementor-toc__toggle-button--collapse\" role=\"button\" tabindex=\"0\" aria-controls=\"elementor-toc__56f4521b\" aria-expanded=\"true\" aria-label=\"Cerrar la tabla de contenidos\"><svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" viewBox=\"0 0 448 512\"><path d=\"M240.971 130.524l194.343 194.343c9.373 9.373 9.373 24.569 0 33.941l-22.667 22.667c-9.357 9.357-24.522 9.375-33.901.04L224 227.495 69.255 381.516c-9.379 9.335-24.544 9.317-33.901-.04l-22.667-22.667c-9.373-9.373-9.373-24.569 0-33.941L207.03 130.525c9.372-9.373 24.568-9.373 33.941-.001z\"><\/path><\/svg><\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<div id=\"elementor-toc__56f4521b\" class=\"elementor-toc__body elementor-toc__list-items--collapsible\">\n\t\t\t<div class=\"elementor-toc__spinner-container\">\n\t\t\t\t<svg class=\"elementor-toc__spinner eicon-animation-spin e-font-icon-svg e-eicon-loading\" aria-hidden=\"true\" viewBox=\"0 0 1000 1000\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M500 975V858C696 858 858 696 858 500S696 142 500 142 142 304 142 500H25C25 237 238 25 500 25S975 237 975 500 763 975 500 975Z\"><\/path><\/svg>\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<section class=\"elementor-section elementor-inner-section elementor-element elementor-element-7ac620ad elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"7ac620ad\" data-element_type=\"section\" data-e-type=\"section\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;}\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-inner-column elementor-element elementor-element-437b7f55\" data-id=\"437b7f55\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-4fcff93b elementor-widget elementor-widget-heading\" data-id=\"4fcff93b\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">Definici\u00f3n y concepto b\u00e1sico<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<div class=\"elementor-element elementor-element-7b535b40 elementor-widget elementor-widget-text-editor\" data-id=\"7b535b40\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p class=\"\" data-start=\"738\" data-end=\"1060\">Un <strong data-start=\"740\" data-end=\"759\">n\u00famero racional<\/strong> es cualquier <strong data-start=\"767\" data-end=\"797\">n\u00famero que pueda escribirse<\/strong> como <strong data-start=\"803\" data-end=\"828\">cociente de dos n\u00fameros enteros<\/strong>. Esto significa que puede <strong data-start=\"851\" data-end=\"876\">expresarse de la forma<\/strong> <em data-start=\"877\" data-end=\"882\">p\/q<\/em>, donde <em data-start=\"890\" data-end=\"893\">p<\/em> y <em data-start=\"898\" data-end=\"901\">q<\/em> son <strong data-start=\"906\" data-end=\"928\">n\u00fameros enteros y q \u2260 0<\/strong>. Por ejemplo, 1\/2, -3, 4,75 e incluso 0 son todos ellos <strong data-start=\"977\" data-end=\"997\">n\u00fameros racionales<\/strong>. Terminan o se repiten cuando se escriben como <strong data-start=\"1047\" data-end=\"1059\">decimales<\/strong>.   <\/p><p class=\"\" data-start=\"1062\" data-end=\"1434\">En cambio, un <strong data-start=\"1078\" data-end=\"1099\">n\u00famero irracional<\/strong> es un <strong data-start=\"1105\" data-end=\"1140\">n\u00famero que no puede expresarse<\/strong> como <strong data-start=\"1146\" data-end=\"1158\">fracci\u00f3n<\/strong> de dos enteros. Estos n\u00fameros tienen expansiones <strong data-start=\"1195\" data-end=\"1237\">decimales que no se repiten ni terminan<\/strong>. <strong data-start=\"1258\" data-end=\"1288\">Algunos ejemplos<\/strong> cl\u00e1sicos de <strong data-start=\"1258\" data-end=\"1288\">n\u00fameros ir<\/strong> racionales son \u03c0 <strong data-start=\"1297\" data-end=\"1307\">(pi)<\/strong>, <strong data-start=\"1309\" data-end=\"1315\">\u221a2<\/strong> y <strong data-start=\"1321\" data-end=\"1343\">el n\u00famero de Euler (e)<\/strong>. Estos n\u00fameros <strong data-start=\"1359\" data-end=\"1380\">no pueden escribirse<\/strong> exactamente como una fracci\u00f3n o un <strong data-start=\"1415\" data-end=\"1433\">n\u00famero decimal<\/strong> simple.   <\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<section class=\"elementor-section elementor-inner-section elementor-element elementor-element-7e71c62d elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"7e71c62d\" data-element_type=\"section\" data-e-type=\"section\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;}\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-inner-column elementor-element elementor-element-14e576c7\" data-id=\"14e576c7\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-7ef093d7 elementor-widget elementor-widget-heading\" data-id=\"7ef093d7\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">Representaci\u00f3n decimal<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<div class=\"elementor-element elementor-element-31abd6d8 elementor-widget elementor-widget-text-editor\" data-id=\"31abd6d8\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p class=\"\" data-start=\"1468\" data-end=\"1690\">El <strong data-start=\"1472\" data-end=\"1489\">punto decimal<\/strong> desempe\u00f1a un papel clave en la distinci\u00f3n de estos dos tipos de n\u00fameros. <strong data-start=\"1553\" data-end=\"1573\">Los n\u00fameros racionales<\/strong> terminan despu\u00e9s de un cierto n\u00famero de <strong data-start=\"1611\" data-end=\"1621\">cifras<\/strong> (por ejemplo, 0,5, 2,75) o entran en un <strong data-start=\"1651\" data-end=\"1672\">patr\u00f3n de repetici\u00f3n<\/strong> (por ejemplo, 0,333&#8230;).<\/p><p class=\"\" data-start=\"1692\" data-end=\"1942\"><strong data-start=\"1692\" data-end=\"1714\">Los n\u00fameros irracionales<\/strong>, en cambio, presentan expansiones <strong data-start=\"1743\" data-end=\"1768\">decimales no repetitivas<\/strong> que se eternizan. Nunca puedes predecir el siguiente <strong data-start=\"1831\" data-end=\"1840\">d\u00edgito<\/strong> de la secuencia. El n\u00famero <strong data-start=\"1869\" data-end=\"1874\">\u03c0<\/strong> es un ejemplo bien conocido: 3,1415926535&#8230;, sin ning\u00fan patr\u00f3n a la vista.  <\/p><p class=\"\" data-start=\"1944\" data-end=\"2085\">As\u00ed, mientras que <strong data-start=\"1956\" data-end=\"1991\">los n\u00fameros racionales pueden escribirse<\/strong> ordenadamente en <strong data-start=\"2002\" data-end=\"2018\">forma decimal<\/strong>, <strong data-start=\"2020\" data-end=\"2049\">los n\u00fameros irracionales no pueden<\/strong> representarse exactamente de esa manera.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<section class=\"elementor-section elementor-inner-section elementor-element elementor-element-4e5dac3e elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"4e5dac3e\" data-element_type=\"section\" data-e-type=\"section\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;}\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-inner-column elementor-element elementor-element-74dab699\" data-id=\"74dab699\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-78f68e8 elementor-widget elementor-widget-heading\" data-id=\"78f68e8\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">Expresiones como fracciones<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<div class=\"elementor-element elementor-element-39408310 elementor-widget elementor-widget-text-editor\" data-id=\"39408310\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p class=\"\" data-start=\"2120\" data-end=\"2411\">Una <strong data-start=\"2128\" data-end=\"2174\">diferencia importante entre los n\u00fameros racionales e irracionales<\/strong> radica en su expresabilidad como <strong data-start=\"2215\" data-end=\"2228\">fracciones<\/strong>. Los <strong data-start=\"2230\" data-end=\"2258\">n\u00fameros racionales incluyen<\/strong> los valores que pueden <strong data-start=\"2278\" data-end=\"2302\">expresarse como cociente<\/strong> de <strong data-start=\"2306\" data-end=\"2322\">dos n\u00fameros enteros<\/strong>. Esto incluye los n\u00fameros positivos, los <strong data-start=\"2356\" data-end=\"2376\">negativos<\/strong>, <strong data-start=\"2378\" data-end=\"2386\">el cero<\/strong> y los decimales que se repiten. <\/p><p class=\"\" data-start=\"2413\" data-end=\"2711\">En cambio, un <strong data-start=\"2429\" data-end=\"2457\">n\u00famero irracional no puede<\/strong> expresarse <strong data-start=\"2461\" data-end=\"2488\">como fracci\u00f3n<\/strong>. N\u00fameros como <strong data-start=\"2503\" data-end=\"2509\">\u221a2<\/strong>, <strong data-start=\"2511\" data-end=\"2516\">\u03c0<\/strong> y <strong data-start=\"2522\" data-end=\"2540\">el n\u00famero de Euler<\/strong> son <strong data-start=\"2545\" data-end=\"2581\">n\u00fameros que no pueden expresarse<\/strong> en la forma <em data-start=\"2594\" data-end=\"2599\">p\/q<\/em>. Aunque pueden aproximarse utilizando decimales, su valor exacto es imposible de captar con una <strong data-start=\"2698\" data-end=\"2710\">fracci\u00f3n<\/strong>.  <\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<section class=\"elementor-section elementor-inner-section elementor-element elementor-element-792ff97b elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"792ff97b\" data-element_type=\"section\" data-e-type=\"section\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;}\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-inner-column elementor-element elementor-element-593f1f99\" data-id=\"593f1f99\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-5d29bf83 elementor-widget elementor-widget-heading\" data-id=\"5d29bf83\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">Ejemplos de cada tipo<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<div class=\"elementor-element elementor-element-56455e05 elementor-widget elementor-widget-text-editor\" data-id=\"56455e05\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p class=\"\" data-start=\"2744\" data-end=\"2845\">Para <strong data-start=\"2747\" data-end=\"2768\">identificar<\/strong> <strong data-start=\"2773\" data-end=\"2803\">ejemplos de n\u00fameros<\/strong> <strong data-start=\"2747\" data-end=\"2768\">racionales<\/strong> e <strong data-start=\"2773\" data-end=\"2803\">irracionales<\/strong>, es \u00fatil fijarse en valores concretos.<\/p><h3 class=\"\" data-start=\"2847\" data-end=\"2880\">Ejemplos de n\u00fameros racionales:<\/h3><ul data-start=\"2881\" data-end=\"3003\"><li class=\"\" data-start=\"2881\" data-end=\"2908\"><p class=\"\" data-start=\"2883\" data-end=\"2908\">5 (puede escribirse como 5\/1)<\/p><\/li><li class=\"\" data-start=\"2909\" data-end=\"2944\"><p class=\"\" data-start=\"2911\" data-end=\"2944\">-2 (tambi\u00e9n un n\u00famero racional, -2\/1)<\/p><\/li><li class=\"\" data-start=\"2945\" data-end=\"2966\"><p class=\"\" data-start=\"2947\" data-end=\"2966\">0,25 (igual a 1\/4)<\/p><\/li><li class=\"\" data-start=\"2967\" data-end=\"3003\"><p class=\"\" data-start=\"2969\" data-end=\"3003\">7,333&#8230; (decimal repetido, 22\/3)<\/p><\/li><\/ul><h3 class=\"\" data-start=\"3005\" data-end=\"3040\">Ejemplos de n\u00fameros irracionales:<\/h3><ul data-start=\"3041\" data-end=\"3229\"><li class=\"\" data-start=\"3041\" data-end=\"3094\"><p class=\"\" data-start=\"3043\" data-end=\"3094\"><strong data-start=\"3043\" data-end=\"3048\">\u03c0<\/strong> (relaci\u00f3n entre la circunferencia y el di\u00e1metro de un c\u00edrculo)<\/p><\/li><li class=\"\" data-start=\"3095\" data-end=\"3130\"><p class=\"\" data-start=\"3097\" data-end=\"3130\"><strong data-start=\"3097\" data-end=\"3103\">\u221a2<\/strong> (la <strong data-start=\"3109\" data-end=\"3124\">ra\u00edz cuadrada<\/strong> de 2)<\/p><\/li><li class=\"\" data-start=\"3131\" data-end=\"3187\"><p class=\"\" data-start=\"3133\" data-end=\"3187\"><strong data-start=\"3133\" data-end=\"3155\">N\u00famero de Euler (e)<\/strong> (base del logaritmo natural)<\/p><\/li><li class=\"\" data-start=\"3188\" data-end=\"3229\"><p class=\"\" data-start=\"3190\" data-end=\"3229\">\u221a3, \u221a5, etc., cuando no es un cuadrado perfecto<\/p><\/li><\/ul><p class=\"\" data-start=\"3231\" data-end=\"3362\">El <strong data-start=\"3235\" data-end=\"3255\">primer<\/strong> n\u00famero <strong data-start=\"3235\" data-end=\"3255\">irracional<\/strong> descubierto fue <strong data-start=\"3283\" data-end=\"3289\">\u221a2<\/strong>, que revel\u00f3 los l\u00edmites de la representaci\u00f3n de <strong data-start=\"3315\" data-end=\"3334\">los n\u00fameros racionales<\/strong> en geometr\u00eda.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<section class=\"elementor-section elementor-inner-section elementor-element elementor-element-65685ed elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"65685ed\" data-element_type=\"section\" data-e-type=\"section\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;}\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-inner-column elementor-element elementor-element-6c76a70\" data-id=\"6c76a70\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-519f8c98 elementor-widget elementor-widget-heading\" data-id=\"519f8c98\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">Clasificaci\u00f3n dentro del sistema de n\u00fameros reales<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<div class=\"elementor-element elementor-element-22e0bcc5 elementor-widget elementor-widget-text-editor\" data-id=\"22e0bcc5\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p class=\"\" data-start=\"3418\" data-end=\"3605\"><strong data-start=\"3423\" data-end=\"3466\">Tanto los n\u00fameros racionales como los irracionales<\/strong> son subconjuntos del <strong data-start=\"3486\" data-end=\"3509\">conjunto de los n\u00fameros reales<\/strong>. Esto significa que <strong data-start=\"3527\" data-end=\"3559\">todos los n\u00fameros son n\u00fameros reales<\/strong>, aunque pertenezcan a categor\u00edas diferentes. <\/p><p class=\"\" data-start=\"3607\" data-end=\"3809\">El <strong data-start=\"3611\" data-end=\"3638\">conjunto de los n\u00fameros racionales<\/strong> incluye <strong data-start=\"3648\" data-end=\"3667\">los n\u00fameros naturales<\/strong>, los <strong data-start=\"3669\" data-end=\"3686\">n\u00fameros enteros<\/strong> y los <strong data-start=\"3692\" data-end=\"3704\">enteros<\/strong>, mientras que <strong data-start=\"3712\" data-end=\"3751\">los n\u00fameros irracionales son n\u00fameros reales<\/strong> que <strong data-start=\"3757\" data-end=\"3780\">no pueden expresarse<\/strong> mediante fracciones o enteros.<\/p><p class=\"\" data-start=\"3811\" data-end=\"3973\">Por eso, cuando te preguntan si un <strong data-start=\"3835\" data-end=\"3857\">n\u00famero es racional<\/strong> o <strong data-start=\"3861\" data-end=\"3875\">irracional<\/strong>, la respuesta puede depender de su comportamiento decimal y de su capacidad para <strong data-start=\"3945\" data-end=\"3972\">expresarse como fracci\u00f3n<\/strong>.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<section class=\"elementor-section elementor-inner-section elementor-element elementor-element-143f2468 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"143f2468\" data-element_type=\"section\" data-e-type=\"section\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;}\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-inner-column elementor-element elementor-element-6147d8c4\" data-id=\"6147d8c4\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-48045560 elementor-widget elementor-widget-heading\" data-id=\"48045560\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">Operaciones matem\u00e1ticas<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<div class=\"elementor-element elementor-element-7e685e8a elementor-widget elementor-widget-text-editor\" data-id=\"7e685e8a\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p class=\"\" data-start=\"4008\" data-end=\"4210\">La interacci\u00f3n de un <strong data-start=\"4029\" data-end=\"4066\">n\u00famero racional y un<\/strong> n\u00famero irracional suele dar como resultado otro <strong data-start=\"4099\" data-end=\"4120\">n\u00famero irracional<\/strong>. Por ejemplo, 2 + \u221a2 es <strong data-start=\"4145\" data-end=\"4159\">irracional<\/strong>, porque la parte irracional no puede eliminarse. <\/p><p class=\"\" data-start=\"4212\" data-end=\"4387\">Sin embargo, la <strong data-start=\"4225\" data-end=\"4246\">suma de un racional<\/strong> y su opuesto exacto irracional (por ejemplo, \u221a2 y -\u221a2) da como resultado un <strong data-start=\"4313\" data-end=\"4332\">n\u00famero racional<\/strong>, concretamente 0. Pero esto es s\u00f3lo en casos especiales. <\/p><p class=\"\" data-start=\"4389\" data-end=\"4613\">Multiplicar <strong data-start=\"4401\" data-end=\"4427\">dos n\u00fameros irracionales<\/strong> puede dar como resultado un <strong data-start=\"4451\" data-end=\"4484\">n\u00famero racional o irracional<\/strong>, dependiendo de los valores. Por ejemplo, \u221a2 \u00d7 \u221a2 = 2, que <strong data-start=\"4543\" data-end=\"4567\">es un n\u00famero racional<\/strong>, a pesar de empezar con componentes irracionales. <\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<section class=\"elementor-section elementor-inner-section elementor-element elementor-element-64989e4 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"64989e4\" data-element_type=\"section\" data-e-type=\"section\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;}\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-inner-column elementor-element elementor-element-143ac909\" data-id=\"143ac909\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-48d4ab0 elementor-widget elementor-widget-heading\" data-id=\"48d4ab0\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">Propiedades y uso<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<div class=\"elementor-element elementor-element-6140a1d3 elementor-widget elementor-widget-text-editor\" data-id=\"6140a1d3\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p class=\"\" data-start=\"4645\" data-end=\"4887\">Las <strong data-start=\"4649\" data-end=\"4690\">propiedades de los<\/strong> n\u00fameros <strong data-start=\"4649\" data-end=\"4690\">racionales e irracionales<\/strong> definen su uso en matem\u00e1ticas y ciencias. Los <strong data-start=\"4744\" data-end=\"4764\">n\u00fameros racionales<\/strong> se utilizan mucho en relaciones, tasas, porcentajes y c\u00e1lculos financieros. Son predecibles y f\u00e1ciles de manejar. <\/p><p class=\"\" data-start=\"4889\" data-end=\"5132\"><strong data-start=\"4889\" data-end=\"4911\">Los n\u00fameros irracionales<\/strong>, aunque m\u00e1s dif\u00edciles de manejar, son fundamentales en geometr\u00eda, f\u00edsica y c\u00e1lculo. El n\u00famero <strong data-start=\"4997\" data-end=\"5002\">\u03c0<\/strong>, por ejemplo, es fundamental para comprender los c\u00edrculos, mientras que <strong data-start=\"5060\" data-end=\"5078\">el n\u00famero de Euler<\/strong> es b\u00e1sico en el crecimiento exponencial y los logaritmos. <\/p><p class=\"\" data-start=\"5134\" data-end=\"5345\">La <strong data-start=\"5138\" data-end=\"5177\">diferencia entre los n\u00fameros racionales<\/strong> y los irracionales tambi\u00e9n radica en la facilidad de uso: <strong data-start=\"5222\" data-end=\"5257\">los n\u00fameros racionales pueden escribirse<\/strong> exactamente, mientras que <strong data-start=\"5273\" data-end=\"5302\">los irracionales no<\/strong>, lo que los hace m\u00e1s abstractos y conceptuales.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<section class=\"elementor-section elementor-inner-section elementor-element elementor-element-5ff4cae elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"5ff4cae\" data-element_type=\"section\" data-e-type=\"section\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;}\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-inner-column elementor-element elementor-element-2746d223\" data-id=\"2746d223\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-f2e3dc2 elementor-widget elementor-widget-heading\" data-id=\"f2e3dc2\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">Conclusi\u00f3n<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<div class=\"elementor-element elementor-element-705aa20e elementor-widget elementor-widget-text-editor\" data-id=\"705aa20e\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p class=\"\" data-start=\"5367\" data-end=\"5728\">La <strong data-start=\"5371\" data-end=\"5417\">diferencia entre<\/strong> n\u00fameros <strong data-start=\"5371\" data-end=\"5417\">racionales e irracionales<\/strong> no es s\u00f3lo una distinci\u00f3n t\u00e9cnica, sino un concepto fundamental para comprender el <strong data-start=\"5511\" data-end=\"5528\">sistema num\u00e9rico<\/strong>. Ambos tipos de n\u00fameros son <strong data-start=\"5556\" data-end=\"5572\">n\u00fameros reales<\/strong> que aparecen en diversos campos de las matem\u00e1ticas y la ciencia, y reconocer sus <strong data-start=\"5646\" data-end=\"5660\">propiedades<\/strong> ayuda a resolver ecuaciones, modelizar situaciones y analizar datos. <\/p><p class=\"\" data-start=\"5730\" data-end=\"6194\">Desde la precisi\u00f3n de una <strong data-start=\"5754\" data-end=\"5766\">fracci\u00f3n<\/strong> hasta el misterio infinito de <strong data-start=\"5794\" data-end=\"5799\">\u03c0<\/strong>, comprender si un <strong data-start=\"5825\" data-end=\"5856\">n\u00famero es un n\u00famero racional<\/strong> o <strong data-start=\"5860\" data-end=\"5884\">un n\u00famero irracional<\/strong> ayuda a descubrir la estructura matem\u00e1tica que subyace al mundo en que vivimos. Tanto si estudias <strong data-start=\"5980\" data-end=\"6014\">los n\u00fameros racionales frente a los irracionales<\/strong> para un examen como si intentas comprender c\u00f3mo se comportan <strong data-start=\"6054\" data-end=\"6073\">los n\u00fameros decimales<\/strong>, la clave est\u00e1 en saber <strong data-start=\"6108\" data-end=\"6120\">clasificar<\/strong>, <strong data-start=\"6122\" data-end=\"6135\">representar<\/strong> y <strong data-start=\"6141\" data-end=\"6154\">trabajar con<\/strong> estas categor\u00edas num\u00e9ricas fundamentales. <\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<section class=\"elementor-section elementor-inner-section elementor-element elementor-element-50915e9a elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"50915e9a\" data-element_type=\"section\" data-e-type=\"section\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;}\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-inner-column elementor-element elementor-element-61f9a927\" data-id=\"61f9a927\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-516b9d8a elementor-widget elementor-widget-heading\" data-id=\"516b9d8a\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-heading-title elementor-size-default\">M\u00e1s informaci\u00f3n sobre la <b>carrera profesional<\/b><\/div>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"<p>El sistema num\u00e9rico es vasto y rico, y consta de distintas categor\u00edas que definen la naturaleza de los valores que utilizamos en matem\u00e1ticas y en la vida real. Entre ellos, los n\u00fameros racionales e irracionales son clasificaciones fundamentales bajo el paraguas de los n\u00fameros reales. Aunque ambos son n\u00fameros reales, difieren significativamente en cuanto a [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":341568,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"elementor_header_footer","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[373,668],"tags":[],"class_list":["post-341576","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-desarrollo-profesional","category-carrera-profesional"],"acf":[],"_links":{"self":[{"href":"https:\/\/barrazacarlos.com\/es\/wp-json\/wp\/v2\/posts\/341576","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/barrazacarlos.com\/es\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/barrazacarlos.com\/es\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/barrazacarlos.com\/es\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/barrazacarlos.com\/es\/wp-json\/wp\/v2\/comments?post=341576"}],"version-history":[{"count":0,"href":"https:\/\/barrazacarlos.com\/es\/wp-json\/wp\/v2\/posts\/341576\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/barrazacarlos.com\/es\/wp-json\/wp\/v2\/media\/341568"}],"wp:attachment":[{"href":"https:\/\/barrazacarlos.com\/es\/wp-json\/wp\/v2\/media?parent=341576"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/barrazacarlos.com\/es\/wp-json\/wp\/v2\/categories?post=341576"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/barrazacarlos.com\/es\/wp-json\/wp\/v2\/tags?post=341576"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}