{"id":8897,"date":"2018-02-08T11:30:54","date_gmt":"2018-02-08T06:00:54","guid":{"rendered":"http:\/\/mycbseguide.com\/blog\/?p=8897"},"modified":"2023-03-22T15:23:01","modified_gmt":"2023-03-22T09:53:01","slug":"real-numbers-class-10-notes-mathematics","status":"publish","type":"post","link":"https:\/\/mycbseguide.com\/blog\/real-numbers-class-10-notes-mathematics\/","title":{"rendered":"Real Numbers class 10 Notes Mathematics"},"content":{"rendered":"<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_76 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\" style=\"cursor:inherit\">Table of Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" aria-label=\"Toggle Table of Content\"><span class=\"ez-toc-js-icon-con\"><span class=\"\"><span class=\"eztoc-hide\" style=\"display:none;\">Toggle<\/span><span class=\"ez-toc-icon-toggle-span\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/span><\/span><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1 eztoc-toggle-hide-by-default' ><ul class='ez-toc-list-level-2' ><li class='ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/mycbseguide.com\/blog\/real-numbers-class-10-notes-mathematics\/#CBSE_Guide_Real_Numbers_class_10_Notes\" >CBSE Guide Real Numbers class 10 Notes<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/mycbseguide.com\/blog\/real-numbers-class-10-notes-mathematics\/#10_Mathematics_notes_Chapter_1_Real_Numbers\" >10 Mathematics notes Chapter 1 Real Numbers<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-1'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/mycbseguide.com\/blog\/real-numbers-class-10-notes-mathematics\/#Download_Revision_Notes_as_PDF\" >Download Revision Notes as PDF<\/a><ul class='ez-toc-list-level-2' ><li class='ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/mycbseguide.com\/blog\/real-numbers-class-10-notes-mathematics\/#Real_Numbers_class_10_Notes\" >Real Numbers class 10 Notes<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/mycbseguide.com\/blog\/real-numbers-class-10-notes-mathematics\/#CBSE_Class-10_Revision_Notes_and_Key_Points\" >CBSE Class-10 Revision Notes and Key Points<\/a><\/li><\/ul><\/li><\/ul><\/nav><\/div>\n<p>CBSE class 10 Mathematics Chapter 1 Real Numbers notes in PDF are available for free download in myCBSEguide mobile app. The best app for CBSE students now provides Real Numbers class 10 Notes latest chapter wise notes for quick preparation of CBSE board exams and school based annual examinations. Class 10 Mathematics notes on chapter 1 Real Numbers are also available for download in CBSE Guide website.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"CBSE_Guide_Real_Numbers_class_10_Notes\"><\/span>CBSE Guide Real Numbers class 10 Notes<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>CBSE guide notes are the comprehensive notes which covers the latest syllabus of CBSE and NCERT. It includes all the topics given in NCERT class 10 Mathematics text book. Users can download CBSE guide quick revision notes from myCBSEguide mobile app and my CBSE guide website.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"10_Mathematics_notes_Chapter_1_Real_Numbers\"><\/span>10 Mathematics notes Chapter 1 Real Numbers<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Download CBSE class 10th revision notes for chapter 1 Real Numbers in PDF format for free. Download revision notes for Real Numbers class 10 Notes and score high in exams. These are the Real Numbers class 10 Notes prepared by team of expert teachers. The revision notes help you revise the whole chapter in minutes. Revising notes in exam days is on of the the best tips recommended by teachers during exam days.<\/p>\n<h1 style=\"text-align: center\"><span class=\"ez-toc-section\" id=\"Download_Revision_Notes_as_PDF\"><\/span><a href=\"https:\/\/mycbseguide.com\/downloads\/cbse-class-10-mathematics\/1202\/cbse-revision-notes\/7\/\">Download Revision Notes as PDF<\/a><span class=\"ez-toc-section-end\"><\/span><\/h1>\n<p style=\"text-align: center\"><strong>CBSE Class\u201310 Mathematics<br \/>\nRevision Notes<br \/>\nCHAPTER 01<br \/>\nREAL NUMBERS <\/strong><\/p>\n<ul>\n<li><strong>Natural numbers<\/strong>: Counting numbers are called Natural numbers. These numbers are denoted by N = {1, 2, 3, &#8230;&#8230;&#8230;}<\/li>\n<li><strong>Whole numbers<\/strong>: The collection of natural numbers along with 0 is the collection of Whole number and is denoted by W.<\/li>\n<li><strong>Integers<\/strong>: The collection of natural numbers, their negatives along with the number zero are called Integers. This collection is denoted by Z.<\/li>\n<li><strong>Rational number<\/strong>: The numbers, which are obtained by dividing two integers, are called Rational numbers. <strong>Division by zero is not defined<\/strong>.<\/li>\n<li><strong>Coprime<\/strong>: If HCF of two numbers is 1, then the two numbers area called relatively prime or coprime.<\/li>\n<\/ul>\n<p>1. <strong>Euclid\u2019s division lemma :<\/strong><\/p>\n<p>For given positive integers \u2018a\u2019 and \u2018b\u2019 there exist unique whole numbers \u2018q\u2019 and \u2018r\u2019 satisfying the relation <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?{\\text{a }} = \\;{\\text{bq }} + \\;{\\text{r}},{\\text{ }}0\\; \\leqslant \\;{\\text{r }} &amp;lt; \\;{\\text{b}}.\" \/><\/span><\/span>.<\/p>\n<p>Theorem: If <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?a\" \/><\/span><\/span>\u00a0and <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?b\" \/><\/span><\/span>\u00a0are non-zero integers, the least positive integer which is expressible as a linear combination of <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?a\" \/><\/span><\/span>\u00a0and <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?b\" \/><\/span><\/span>\u00a0is the HCF of <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?a\" \/><\/span><\/span>\u00a0and <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?b\" \/><\/span><\/span>, i.e., if <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?d\" \/><\/span><\/span>\u00a0is the HCF of <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?a\" \/><\/span><\/span>\u00a0and <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?b\" \/><\/span><\/span>, then these exist integers <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?x_1\" \/><\/span><\/span>\u00a0and <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?y_1\" \/><\/span><\/span>, such that <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?d = a{x_1} + b{y_1}\" \/><\/span><\/span>\u00a0and <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?d\" \/><\/span><\/span>\u00a0is the smallest positive integer which is expressible in this form.<\/p>\n<p>The HCF of <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?a\" \/><\/span><\/span>\u00a0and <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?b\" \/><\/span><\/span>\u00a0is denoted by HCF<span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?\\left( {a,b} \\right)\" \/><\/span><\/span>.<\/p>\n<p>2. <strong>Euclid\u2019s division algorithms :<\/strong><\/p>\n<p>HCF of any two positive integers a and b. With a &gt; b is obtained as follows:<\/p>\n<p><strong>Step 1<\/strong> : Apply Euclid\u2019s division lemma to a and b to find q and r such that<\/p>\n<p><span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?{\\text{a }} = \\;{\\text{bq }} + \\;{\\text{r}}\\;,{\\text{ }}0\\; \\leqslant \\;{\\text{r }} &amp;lt; \\;{\\text{b}}.\" \/><\/span><\/span><\/p>\n<p>b = Divisor<\/p>\n<p>q = Quotient<\/p>\n<p>r =\u00a0 Remainder<\/p>\n<p><strong>Step II<\/strong>: If r\u00a0 = 0, HCF (a,b)=b if <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?r \\ne 0\" \/><\/span><\/span>, apply Euclid\u2019s lemma to b and r.<\/p>\n<p><strong>Step III:<\/strong> Continue the process till the remainder is zero. The divisor at this stage will be the required HCF.<\/p>\n<p>3. <strong>The Fundamental Theorem of Arithmetic :<\/strong><\/p>\n<p>Every composite number can be expressed (factorized) as a product of primes and this factorization is unique, apart from the order in which the prime factors occur.<\/p>\n<p><span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?Ex:\\;\\;24 = 2 \\times 2 \\times 2 \\times 3 = 3 \\times 2 \\times 2 \\times 2\" \/><\/span><\/span><\/p>\n<p>4. Let <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?x = {p \\over q},\" \/><\/span><\/span>\u00a0<span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?q \\ne 0\" \/><\/span><\/span>\u00a0 to be a rational number, such that the prime factorization of \u2018q\u2019 is of the form 2m+5n, where m, n are non-negative integers. Then x has a decimal expansion which is terminating.<\/p>\n<p>5. Let <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?x = \\frac{p}{q},\\;\\;q \\ne 0\" \/><\/span><\/span>\u00a0be a rational number, such that the prime factorization of q is not of the form 2m+5n, where m, n are non-negative integers. Then x has a decimal expansion which is non-terminating repeating.<\/p>\n<p>6. <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?\\sqrt p\" \/><\/span><\/span>\u00a0is irrational, which p is a prime. A number is called irrational if it cannot be written in the form <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?\\frac{P}{q}\" \/><\/span><\/span>\u00a0where p and q are integers and <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?{\\text{q}}\\;\\,\\, \\ne {\\text{ }}0.\" \/><\/span><\/span><\/p>\n<p>8. If a and b are two positive integers, then HCF(a, b) x LCM(a, b) = a x b<\/p>\n<p>i.e., (HCF x LCM) of two intergers = Product of intergers.<\/p>\n<p>9. A rational number which when expressed in the lowest term has factors 2 or 5 in the denominator can be written as terminating decimal otherwise a non-terminating recurring decimal. In other words, if the rational number <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?{a \\over b}\" \/><\/span><\/span>\u00a0is, such that the prime factorization of b is of form <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?{2^m}{.5^n},\" \/><\/span><\/span>\u00a0where m and n are natural numbers, then <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?{a \\over b}\" \/><\/span><\/span>\u00a0has a terminating decimal expansion.<\/p>\n<p>10. We conclude that every rational number can be represented in the form of terminating or non-terminating recurring decimal.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Real_Numbers_class_10_Notes\"><\/span>Real Numbers class 10 Notes<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<ul>\n<li>CBSE Revision notes (PDF Download) Free<\/li>\n<li>CBSE Revision notes for Class 10 Mathematics PDF<\/li>\n<li>CBSE Revision notes Class 10 Mathematics \u2013 CBSE<\/li>\n<li>CBSE Revisions notes and Key Points Class 10 Mathematics<\/li>\n<li>Summary of the NCERT books all chapters in Mathematics class 10<\/li>\n<li>Short notes for CBSE class 10th Mathematics<\/li>\n<li>Key notes and chapter summary of Mathematics class 10<\/li>\n<li>Quick revision notes for CBSE board exams<\/li>\n<\/ul>\n<h2><span class=\"ez-toc-section\" id=\"CBSE_Class-10_Revision_Notes_and_Key_Points\"><\/span><strong>CBSE Class-10 Revision Notes and Key Points<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Real Numbers class 10 Notes. CBSE quick revision note for Class-10 Mathematics, Chemistry, Maths, Biology and other subject are very helpful to revise the whole syllabus during exam days. The revision notes covers all important formulas and concepts given in the chapter. Even if you wish to have an overview of a chapter, quick revision notes are here to do if for you. These notes will certainly save your time during stressful exam days.<\/p>\n<ul>\n<li><a href=\"http:\/\/mycbseguide.com\/downloads\/cbse-class-10-mathematics\/1202\/cbse-revision-notes\/7\/\">Revision Notes for class-10 Mathematics<\/a><\/li>\n<li><a href=\"http:\/\/mycbseguide.com\/downloads\/cbse-class-10-science\/1176\/cbse-revision-notes\/7\/\">Revision Notes for class-10 Science<\/a><\/li>\n<li><a href=\"http:\/\/mycbseguide.com\/downloads\/cbse-class-10-social-science\/1896\/cbse-revision-notes\/7\/\">Revision Notes for class-10 Social Science<\/a><\/li>\n<li><a href=\"http:\/\/mycbseguide.com\/downloads\/cbse-class-10-english-communicative\/1901\/cbse-revision-notes\/7\/\">Revision Notes for class-10 English Communicative<\/a><\/li>\n<\/ul>\n<p>To download Real Numbers class 10 Notes, sample paper for class 10 Mathematics, Social Science, Science, English Communicative; do check myCBSEguide app or website. myCBSEguide provides sample papers with solution, test papers for chapter-wise practice, NCERT solutions, NCERT Exemplar solutions, quick revision notes for ready reference, CBSE guess papers and CBSE important question papers. Sample Paper all are made available through\u00a0<a href=\"https:\/\/play.google.com\/store\/apps\/details?id=in.techchefs.MyCBSEGuide&amp;referrer=utm_source%3Dmycbse_bottom%26utm_medium%3Dtext%26utm_campaign%3Dmycbseads\"><strong>the best app for CBSE students<\/strong><\/a>\u00a0and myCBSEguide website.<\/p>\n<ul>\n<li class=\"entry-title\"><a href=\"https:\/\/mycbseguide.com\/blog\/real-numbers-class-10-notes-mathematics\/\">Real Numbers class 10 Notes Mathematics<\/a><\/li>\n<li class=\"entry-title\"><a href=\"https:\/\/mycbseguide.com\/blog\/polynomials-class-10-notes-mathematics\/\">Polynomials class 10 Notes Mathematics<\/a><\/li>\n<li class=\"entry-title\"><a href=\"https:\/\/mycbseguide.com\/blog\/pair-linear-equations-two-variables-class-10-notes-mathematics\/\">Pair of Linear Equations in Two Variables class 10 Notes Mathematics<\/a><\/li>\n<li class=\"entry-title\"><a href=\"https:\/\/mycbseguide.com\/blog\/quadratic-equations-class-10-notes-mathematics\/\">Quadratic Equations class 10 Notes Mathematics<\/a><\/li>\n<li class=\"entry-title\"><a href=\"https:\/\/mycbseguide.com\/blog\/arithmetic-progressions-class-10-notes-mathematics\/\">Arithmetic Progressions class 10 Notes Mathematics<\/a><\/li>\n<li class=\"entry-title\"><a href=\"https:\/\/mycbseguide.com\/blog\/triangles-class-10-notes-mathematics\/\">Triangles class 10 Notes Mathematics<\/a><\/li>\n<li class=\"entry-title\"><a href=\"https:\/\/mycbseguide.com\/blog\/coordinate-geometry-class-10-notes-mathematics\/\">Coordinate Geometry class 10 Notes Mathematics<\/a><\/li>\n<li class=\"entry-title\"><a href=\"https:\/\/mycbseguide.com\/blog\/introduction-trigonometry-class-10-notes-mathematics\/\">Introduction to Trigonometry class 10 Notes Mathematics<\/a><\/li>\n<li class=\"entry-title\"><a href=\"https:\/\/mycbseguide.com\/blog\/applications-trigonometry-class-10-notes-mathematics\/\">Some Applications of Trigonometry class 10 Notes Mathematics<\/a><\/li>\n<li class=\"entry-title\"><a href=\"https:\/\/mycbseguide.com\/blog\/circles-class-10-notes-mathematics\/\">Circles class 10 Notes Mathematics<\/a><\/li>\n<li class=\"entry-title\"><a href=\"https:\/\/mycbseguide.com\/blog\/constructions-class-10-notes-mathematics\/\">Constructions class 10 Notes Mathematics<\/a><\/li>\n<li class=\"entry-title\"><a href=\"https:\/\/mycbseguide.com\/blog\/area-related-circles-class-10-notes-mathematics\/\">Area Related to Circles class 10 Notes Mathematics<\/a><\/li>\n<li class=\"entry-title\"><a href=\"https:\/\/mycbseguide.com\/blog\/surface-areas-volumes-class-10-notes-mathematics\/\">Surface Areas and Volumes class 10 Notes Mathematic<\/a><\/li>\n<li class=\"entry-title\"><a href=\"https:\/\/mycbseguide.com\/blog\/statistics-class-10-notes-mathematics\/\">Statistics class 10 Notes Mathematics<\/a><\/li>\n<li class=\"entry-title\"><a href=\"https:\/\/mycbseguide.com\/blog\/probability-class-10-notes-mathematics\/\">Probability class 10 Notes Mathematics<\/a><\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>CBSE class 10 Mathematics Chapter 1 Real Numbers notes in PDF are available for free download in myCBSEguide mobile app. The best app for CBSE students now provides Real Numbers class 10 Notes latest chapter wise notes for quick preparation of CBSE board exams and school based annual examinations. Class 10 Mathematics notes on chapter &#8230; <a title=\"Real Numbers class 10 Notes Mathematics\" class=\"read-more\" href=\"https:\/\/mycbseguide.com\/blog\/real-numbers-class-10-notes-mathematics\/\" aria-label=\"More on Real Numbers class 10 Notes Mathematics\">Read more<\/a><\/p>\n","protected":false},"author":2,"featured_media":8899,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[46,456],"tags":[1042,457,150,1541,461,426,240,460],"class_list":["post-8897","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-cbse-class-10","category-revision-notes","tag-cbse-class-10-mathematics","tag-cbse-notes","tag-cbse-notes-and-key-points","tag-cbse-revision-notes","tag-mathematics-notes","tag-quick-revision","tag-quick-revision-notes","tag-real-numbers"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v26.0 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Real Numbers class 10 Notes Mathematics | myCBSEguide<\/title>\n<meta name=\"description\" content=\"Real Numbers class 10 Notes Mathematics chapter 1 in PDF format for free download. 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