{"id":9669,"date":"2018-02-13T14:17:57","date_gmt":"2018-02-13T08:47:57","guid":{"rendered":"http:\/\/mycbseguide.com\/blog\/?p=9669"},"modified":"2018-03-19T14:10:42","modified_gmt":"2018-03-19T08:40:42","slug":"number-systems-class-9-notes-mathematics","status":"publish","type":"post","link":"https:\/\/mycbseguide.com\/blog\/number-systems-class-9-notes-mathematics\/","title":{"rendered":"Number Systems class 9 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\/number-systems-class-9-notes-mathematics\/#CBSE_Guide_Number_Systems_class_9_Notes\" >CBSE Guide Number Systems class 9 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\/number-systems-class-9-notes-mathematics\/#9_Mathematics_notes_Chapter_1_Number_Systems\" >9 Mathematics notes Chapter 1 Number Systems<\/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\/number-systems-class-9-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\/number-systems-class-9-notes-mathematics\/#Number_Systems_class_9_Notes\" >Number Systems class 9 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\/number-systems-class-9-notes-mathematics\/#CBSE_Class-9_Revision_Notes_and_Key_Points\" >CBSE Class-9 Revision Notes and Key Points<\/a><\/li><\/ul><\/li><\/ul><\/nav><\/div>\n<p>CBSE class 9 Mathematics Chapter 1 Number Systems notes in PDF are available for free download in myCBSEguide mobile app. The best app for CBSE students now provides Number Systems class 9 Notes latest chapter wise notes for quick preparation of CBSE exams and school based annual examinations. Class 9 Mathematics notes on Chapter 1 Number Systems are also available for download in CBSE Guide website.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"CBSE_Guide_Number_Systems_class_9_Notes\"><\/span>CBSE Guide Number Systems class 9 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 9 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=\"9_Mathematics_notes_Chapter_1_Number_Systems\"><\/span>9 Mathematics notes Chapter 1 Number Systems<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Download CBSE class 9th revision notes for Chapter 1 Number Systems in PDF format for free. Download revision notes for Number Systems class 9 Notes and score high in exams. These are the Number Systems class 9 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 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><strong><a href=\"https:\/\/mycbseguide.com\/downloads\/cbse-class-09-mathematics\/1234\/cbse-revision-notes\/7\/\">Download Revision Notes as PDF<\/a><\/strong><span class=\"ez-toc-section-end\"><\/span><\/h1>\n<p style=\"text-align: center\"><strong>CBSE Class 09 Mathematics<br \/>\nRevision Notes<br \/>\nCHAPTER \u2013 1<br \/>\nNUMBER SYSTEMS<\/strong><\/p>\n<p>1 Rational Numbers<\/p>\n<p>2 Irrational Numbers<\/p>\n<p>3 Real Numbers and their Decimal Expansions<\/p>\n<p>4 Operations on Real Numbers<\/p>\n<p>5 Laws of Exponents for Real Numbers<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/revise\/09\/math\/09_math_ch01_01.jpg\" \/><\/p>\n<ul>\n<li>Natural numbers are\u00a0:\u00a01, 2, 3, \u2026\u2026\u2026\u2026\u2026.. denoted by N.<\/li>\n<li>Whole numbers are\u00a0: 0, 1, 2, 3, \u2026\u2026\u2026\u2026\u2026\u2026 denoted by W.<\/li>\n<li>Integers\u00a0: \u2026\u2026. -3, -2, -1, 0, 1, 2, 3, \u2026\u2026\u2026\u2026\u2026\u2026 denoted by Z.<\/li>\n<li>Rational numbers &#8211; All the numbers which can 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?{p \\over q}\" \/><\/span><\/span>\u00a0are called rational numbers where 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?q \\ne 0.\" \/><\/span><\/span>\u00a0Every integer p is also a rational number, can be written as <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?{p \\over 1}.\" \/><\/span><\/span><\/li>\n<li>Irrational numbers &#8211; A number\u00a0is 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?{p \\over q}\" \/><\/span><\/span>\u00a0 where 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?q \\ne 0.\" \/><\/span><\/span><\/li>\n<li>The decimal expansion of a rational number is either terminating or non terminating recurring. Thus we say that a number whose decimal expansion is either terminating or non terminating recurring is a rational number.<\/li>\n<li>Terminating decimals: The rational numbers with a finite decimal part or for which the long division terminates after a finite number of steps are known as finite or terminating decimals.<\/li>\n<li>Non-Terminating decimals: The rational numbers with an infinite decimal part or for which the long division does not terminate\u00a0even\u00a0after an infinite number of steps are known as infinite or non-terminating decimals<\/li>\n<li>The decimal expansion of a irrational number is non terminating non recurring.<\/li>\n<li>All the rational numbers and irrational numbers taken together\u00a0make a collection of real numbers.<\/li>\n<li>A real number is either rational or irrational.<\/li>\n<li>If r is rational and s is irrational then r+s, r\u2013s, r.s are always irrational numbers but <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 \\over s}\" \/><\/span><\/span>\u00a0may be rational or irrational.<\/li>\n<li>If n is a natural number other than a perfect square, 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?\\sqrt n\" \/><\/span><\/span>\u00a0is a irrational number.<\/li>\n<li>Negative of an irrational number is an irrational number.<\/li>\n<li>There is a real number corresponding to every point on the number line. Also, corresponding to every real number there is a point on the number line.<\/li>\n<li>Every irrational number can be represented on a number line using Pythagoras theorem.<\/li>\n<li>For every positive real 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?x,\" \/><\/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?\\sqrt x\" \/><\/span><\/span>\u00a0can be represented by a point on the number line by using the following steps:<\/li>\n<\/ul>\n<ol>\n<li>Obtain all positive real numbers <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\" \/><\/span><\/span>\u00a0(say).<\/li>\n<li>Draw a line and mark a point P on it.<\/li>\n<li>Make a point Q on the line such that PQ = <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\" \/><\/span><\/span>\u00a0units.<\/li>\n<li>From point Q marka distance of 1 unit and mark the new point as R.<\/li>\n<li>Find the mid-point of PR and mark the point as O.<\/li>\n<li>Draw a circle with centre O and radius OR.<\/li>\n<li>Draw a line perpendicular to PR passing through Q and intersecting the semi-circle at S. Length QS is equal to <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 x\" \/><\/span><\/span><\/li>\n<\/ol>\n<ul>\n<li>Rationalization means to remove square root from the denominator.<\/li>\n<\/ul>\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?\\frac{{3 + \\sqrt5 }}{{\\sqrt 2 }}\" \/><\/span><\/span>\u00a0to remove we will multiply both numerator &amp; denominator by <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 2\" \/><\/span><\/span><\/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?{1 \\over {a \\pm \\sqrt b }}\" \/><\/span><\/span>\u00a0 its rationalization factor <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 \\mp \\sqrt b\" \/><\/span><\/span><\/p>\n<h2><span class=\"ez-toc-section\" id=\"Number_Systems_class_9_Notes\"><\/span>Number Systems class 9 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 9 Mathematics PDF<\/li>\n<li>CBSE Revision notes Class 9 Mathematics \u2013 CBSE<\/li>\n<li>CBSE Revisions notes and Key Points Class 9 Mathematics<\/li>\n<li>Summary of the NCERT books all chapters in Mathematics class 9<\/li>\n<li>Short notes for CBSE class 9th Mathematics<\/li>\n<li>Key notes and chapter summary of Mathematics class 9<\/li>\n<li>Quick revision notes for CBSE board exams<\/li>\n<\/ul>\n<h2><span class=\"ez-toc-section\" id=\"CBSE_Class-9_Revision_Notes_and_Key_Points\"><\/span><strong>CBSE Class-9 Revision Notes and Key Points<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Number Systems class 9 Notes. CBSE quick revision note for Class-9 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-09-mathematics\/1234\/cbse-revision-notes\/7\/\">Revision Notes for class-09 Mathematics<\/a><\/li>\n<li><a href=\"http:\/\/mycbseguide.com\/downloads\/cbse-class-09-science\/1218\/cbse-revision-notes\/7\/\">Revision Notes for class-09 Science<\/a><\/li>\n<li><a href=\"http:\/\/mycbseguide.com\/downloads\/cbse-class-09-social-science\/1895\/cbse-revision-notes\/7\/\">Revision Notes for class-09 Social Science<\/a><\/li>\n<li><a href=\"http:\/\/mycbseguide.com\/downloads\/cbse-class-09-english-communicative\/1900\/cbse-revision-notes\/7\/\">Revision Notes for class-09 English Communicative<\/a><\/li>\n<\/ul>\n<p>To download Number Systems class 9 Notes, sample paper for class 9 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\/number-systems-class-9-notes-mathematics\/\">Number Systems class 9 Notes Mathematics<\/a><\/li>\n<li class=\"entry-title\"><a href=\"https:\/\/mycbseguide.com\/blog\/polynomials-class-9-notes-mathematics\/\">Polynomials class 9 Notes Mathematics<\/a><\/li>\n<li class=\"entry-title\"><a href=\"https:\/\/mycbseguide.com\/blog\/coordinate-geometry-class-9-notes-mathematics\/\">Coordinate Geometry class 9 Notes Mathematics<\/a><\/li>\n<li class=\"entry-title\"><a href=\"https:\/\/mycbseguide.com\/blog\/linear-equations-two-variables-class-9-notes-mathematics\/\">Linear Equations in Two Variables class 9 Notes Mathematics<\/a><\/li>\n<li class=\"entry-title\"><a href=\"https:\/\/mycbseguide.com\/blog\/introduction-euclids-geometry-class-9-notes-mathematics\/\">Introduction to Euclids Geometry class 9 Notes Mathematics<\/a><\/li>\n<li class=\"entry-title\"><a href=\"https:\/\/mycbseguide.com\/blog\/lines-angles-class-9-notes-mathematics\/\">Lines and Angles class 9 Notes Mathematics<\/a><\/li>\n<li class=\"entry-title\"><a href=\"https:\/\/mycbseguide.com\/blog\/triangles-class-9-notes-mathematics\/\">Triangles class 9 Notes Mathematics<\/a><\/li>\n<li class=\"entry-title\"><a href=\"https:\/\/mycbseguide.com\/blog\/quadrilaterals-class-9-notes-mathematics\/\">Quadrilaterals class 9 Notes Mathematics<\/a><\/li>\n<li class=\"entry-title\"><a href=\"https:\/\/mycbseguide.com\/blog\/areas-parallelograms-triangles-class-9-notes-mathematics-2\/\">Areas of Parallelograms and Triangles class 9 Notes Mathematics<\/a><\/li>\n<li class=\"entry-title\"><a href=\"https:\/\/mycbseguide.com\/blog\/circles-class-9-notes-mathematics\/\">Circles class 9 Notes Mathematics<\/a><\/li>\n<li class=\"entry-title\"><a href=\"https:\/\/mycbseguide.com\/blog\/constructions-class-9-notes-mathematics\/\">Constructions class 9 Notes Mathematics<\/a><\/li>\n<li class=\"entry-title\"><a href=\"https:\/\/mycbseguide.com\/blog\/herons-formula-class-9-notes-mathematics\/\">Herons Formula class 9 Notes Mathematics<\/a><\/li>\n<li class=\"entry-title\"><a href=\"https:\/\/mycbseguide.com\/blog\/surface-areas-volumes-class-9-notes-mathematics\/\">Surface Areas and Volumes class 9 Notes Mathematics<\/a><\/li>\n<li class=\"entry-title\"><a href=\"https:\/\/mycbseguide.com\/blog\/statistics-class-9-notes-mathematics\/\">Statistics class 9 Notes Mathematics<\/a><\/li>\n<li class=\"entry-title\"><a href=\"https:\/\/mycbseguide.com\/blog\/probability-class-9-notes-mathematics\/\">Probability class 9 Notes Mathematics<\/a><\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>CBSE class 9 Mathematics Chapter 1 Number Systems notes in PDF are available for free download in myCBSEguide mobile app. The best app for CBSE students now provides Number Systems class 9 Notes latest chapter wise notes for quick preparation of CBSE exams and school based annual examinations. Class 9 Mathematics notes on Chapter 1 &#8230; <a title=\"Number Systems class 9 Notes Mathematics\" class=\"read-more\" href=\"https:\/\/mycbseguide.com\/blog\/number-systems-class-9-notes-mathematics\/\" aria-label=\"More on Number Systems class 9 Notes Mathematics\">Read more<\/a><\/p>\n","protected":false},"author":2,"featured_media":9670,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[45,456],"tags":[457,150,681,426,240],"class_list":["post-9669","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-cbse-class-09","category-revision-notes","tag-cbse-notes","tag-cbse-notes-and-key-points","tag-number-systems","tag-quick-revision","tag-quick-revision-notes"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v26.0 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Number Systems class 9 Notes Mathematics | myCBSEguide<\/title>\n<meta name=\"description\" content=\"Number Systems class 9 Notes Mathematics chapter 1 in PDF format for free download. 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