{"id":3345,"date":"2026-06-04T12:52:11","date_gmt":"2026-06-04T07:22:11","guid":{"rendered":"https:\/\/mymockmate.com\/notes\/?p=3345"},"modified":"2026-06-04T13:17:37","modified_gmt":"2026-06-04T07:47:37","slug":"ncert-class-9-maths-end-of-chapter-the-world-of-numbers-solutions","status":"publish","type":"post","link":"https:\/\/mymockmate.com\/notes\/ncert-class-9-maths-end-of-chapter-the-world-of-numbers-solutions\/","title":{"rendered":"NCERT Class 9 Maths End-of-Chapter (The World of Numbers) Solutions"},"content":{"rendered":"<div class=\"pdfprnt-buttons pdfprnt-buttons-post pdfprnt-top-bottom-right\"><a href=\"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/posts\/3345?print=print\" class=\"pdfprnt-button pdfprnt-button-print\" target=\"_blank\" ><img decoding=\"async\" src=\"https:\/\/mymockmate.com\/notes\/wp-content\/plugins\/pdf-print\/images\/print.png\" alt=\"image_print\" title=\"Print Content\" \/><span class=\"pdfprnt-button-title pdfprnt-button-print-title\">Print<\/span><\/a> <span class=\"pdfprnt-count-generation\"><\/span><\/div>\n<h1 class=\"wp-block-heading\">Short Introduction<\/h1>\n\n\n\n<p class=\"wp-block-paragraph\">The End-of-Chapter Exercises of Chapter 3 &#8220;The World of Numbers&#8221; help students strengthen their understanding of rational numbers, irrational numbers, decimal expansions, and number line representation. In this article, we provide detailed step-by-step solutions for Questions 1 to 6 in a simple and exam-oriented manner.<\/p>\n\n\n\n<h1 class=\"wp-block-heading\">Quick Information Box<\/h1>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Chapter:<\/strong> The World of Numbers<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Class:<\/strong> Grade 9 Mathematics<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Exercise:<\/strong> End-of-Chapter Exercises (Part 1)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Questions Covered:<\/strong> Q.1 to Q.6<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Main Topics:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Terminating and Repeating Decimals<\/li>\n\n\n\n<li>Irrational Numbers<\/li>\n\n\n\n<li>Conversion of Decimals into Fractions<\/li>\n\n\n\n<li>Number Line Representation<\/li>\n\n\n\n<li>Rational Numbers Between Two Numbers<\/li>\n<\/ul>\n\n\n\n<h1 class=\"wp-block-heading\">Concepts Used (Topics Covered)<\/h1>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Rational Numbers<\/li>\n\n\n\n<li>Irrational Numbers<\/li>\n\n\n\n<li>Decimal Expansion<\/li>\n\n\n\n<li>Long Division Method<\/li>\n\n\n\n<li>Fraction Conversion<\/li>\n\n\n\n<li>Number Line Representation<\/li>\n\n\n\n<li>Finding Rational Numbers Between Two Numbers<\/li>\n<\/ul>\n\n\n\n<h1 class=\"wp-block-heading\">Important Formulas<\/h1>\n\n\n\n<h3 class=\"wp-block-heading\">1. Rational Number<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">A number of the form:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">p\/q, where q \u2260 0<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">2. Terminating Decimal Test<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">If the denominator (in lowest form) contains only prime factors 2 and\/or 5, then the decimal expansion terminates.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">3. Repeating Decimal Test<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">If the denominator contains any prime factor other than 2 or 5, the decimal expansion is non-terminating repeating.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">4. Converting Decimal into Fraction<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Decimal \u00d7 10\u207f \/ 10\u207f<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">where n = number of decimal places.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h1 class=\"wp-block-heading\">Question 1<\/h1>\n\n\n\n<h2 class=\"wp-block-heading\">Convert the following rational numbers into terminating or non-terminating repeating decimals by long division:<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">Solution<\/h3>\n\n\n\n<figure class=\"wp-block-image size-large\"><img fetchpriority=\"high\" decoding=\"async\" width=\"1024\" height=\"683\" src=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-16-1024x683.png\" alt=\"image\" class=\"wp-image-3352\" title=\"NCERT Class 9 Maths End-of-Chapter (The World of Numbers) Solutions\" srcset=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-16-1024x683.png 1024w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-16-300x200.png 300w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-16-768x512.png 768w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-16.png 1536w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h1 class=\"wp-block-heading\">Question 2<\/h1>\n\n\n\n<h2 class=\"wp-block-heading\">Prove that \u221a5 is an irrational number.<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">Solution<\/h3>\n\n\n\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" width=\"1024\" height=\"683\" src=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-15-1024x683.png\" alt=\"image\" class=\"wp-image-3351\" title=\"NCERT Class 9 Maths End-of-Chapter (The World of Numbers) Solutions\" srcset=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-15-1024x683.png 1024w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-15-300x200.png 300w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-15-768x512.png 768w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-15.png 1536w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h1 class=\"wp-block-heading\">Question 3<\/h1>\n\n\n\n<h2 class=\"wp-block-heading\">Convert the following decimal numbers into p\/q form.<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\"><\/h3>\n\n\n\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" width=\"1024\" height=\"683\" src=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-17-1024x683.png\" alt=\"image\" class=\"wp-image-3353\" title=\"NCERT Class 9 Maths End-of-Chapter (The World of Numbers) Solutions\" srcset=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-17-1024x683.png 1024w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-17-300x200.png 300w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-17-768x512.png 768w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-17.png 1536w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h1 class=\"wp-block-heading\">Question 4<\/h1>\n\n\n\n<h2 class=\"wp-block-heading\">Locate the following rational numbers on the number line.<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\"><\/h3>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"683\" src=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-18-1024x683.png\" alt=\"image\" class=\"wp-image-3354\" title=\"NCERT Class 9 Maths End-of-Chapter (The World of Numbers) Solutions\" srcset=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-18-1024x683.png 1024w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-18-300x200.png 300w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-18-768x512.png 768w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-18.png 1536w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h1 class=\"wp-block-heading\">Question 5<\/h1>\n\n\n\n<h2 class=\"wp-block-heading\">Find six rational numbers between 3 and 4.<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">Solution<\/h3>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"683\" src=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-19-1024x683.png\" alt=\"image\" class=\"wp-image-3355\" title=\"NCERT Class 9 Maths End-of-Chapter (The World of Numbers) Solutions\" srcset=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-19-1024x683.png 1024w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-19-300x200.png 300w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-19-768x512.png 768w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-19.png 1536w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h1 class=\"wp-block-heading\">Question 6<\/h1>\n\n\n\n<h2 class=\"wp-block-heading\">Find five rational numbers between 2\/5 and 3\/5.<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">Solution<\/h3>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"683\" src=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-20-1024x683.png\" alt=\"image\" class=\"wp-image-3356\" title=\"NCERT Class 9 Maths End-of-Chapter (The World of Numbers) Solutions\" srcset=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-20-1024x683.png 1024w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-20-300x200.png 300w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-20-768x512.png 768w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-20.png 1536w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<ol start=\"7\" class=\"wp-block-list\">\n<li><\/li>\n<\/ol>\n\n\n\n<p class=\"has-x-large-font-size wp-block-paragraph\"><strong>Question 7<\/strong><\/p>\n\n\n\n<p class=\"has-medium-font-size wp-block-paragraph\"><strong>Find 5 rational numbers between1\/6 and 2\/5 .<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Solution :<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"683\" src=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-21-1024x683.png\" alt=\"image\" class=\"wp-image-3358\" title=\"NCERT Class 9 Maths End-of-Chapter (The World of Numbers) Solutions\" srcset=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-21-1024x683.png 1024w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-21-300x200.png 300w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-21-768x512.png 768w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-21.png 1536w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<p class=\"has-x-large-font-size wp-block-paragraph\"><strong>Question 8<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"488\" height=\"59\" src=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-22.png\" alt=\"image\" class=\"wp-image-3359\" title=\"NCERT Class 9 Maths End-of-Chapter (The World of Numbers) Solutions\" srcset=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-22.png 488w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-22-300x36.png 300w\" sizes=\"(max-width: 488px) 100vw, 488px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"819\" src=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-23-1024x819.png\" alt=\"image\" class=\"wp-image-3360\" title=\"NCERT Class 9 Maths End-of-Chapter (The World of Numbers) Solutions\" srcset=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-23-1024x819.png 1024w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-23-300x240.png 300w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-23-768x615.png 768w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-23.png 1402w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<p class=\"has-x-large-font-size wp-block-paragraph\"><strong>Question 9<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Let a and b be two non-zero rational numbers such that a + (1\/ b) = 0. Without assigning any numerical values, determine whether ab is positive or negative. Justify your answer<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"683\" src=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-24-1024x683.png\" alt=\"image\" class=\"wp-image-3363\" title=\"NCERT Class 9 Maths End-of-Chapter (The World of Numbers) Solutions\" srcset=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-24-1024x683.png 1024w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-24-300x200.png 300w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-24-768x512.png 768w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-24.png 1536w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<p class=\"has-x-large-font-size wp-block-paragraph\"><strong>Question 10<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"746\" height=\"174\" src=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-25.png\" alt=\"image\" class=\"wp-image-3365\" title=\"NCERT Class 9 Maths End-of-Chapter (The World of Numbers) Solutions\" srcset=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-25.png 746w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-25-300x70.png 300w\" sizes=\"(max-width: 746px) 100vw, 746px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"683\" src=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-26-1024x683.png\" alt=\"image\" class=\"wp-image-3367\" title=\"NCERT Class 9 Maths End-of-Chapter (The World of Numbers) Solutions\" srcset=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-26-1024x683.png 1024w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-26-300x200.png 300w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-26-768x512.png 768w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-26.png 1536w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<p class=\"has-x-large-font-size wp-block-paragraph\"><strong>Question 11<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"740\" height=\"103\" src=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-27.png\" alt=\"image\" class=\"wp-image-3368\" title=\"NCERT Class 9 Maths End-of-Chapter (The World of Numbers) Solutions\" srcset=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-27.png 740w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-27-300x42.png 300w\" sizes=\"(max-width: 740px) 100vw, 740px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"683\" src=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-30-1024x683.png\" alt=\"image\" class=\"wp-image-3371\" title=\"NCERT Class 9 Maths End-of-Chapter (The World of Numbers) Solutions\" srcset=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-30-1024x683.png 1024w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-30-300x200.png 300w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-30-768x512.png 768w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-30.png 1536w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<p class=\"has-x-large-font-size wp-block-paragraph\"><strong>Question 12<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"743\" height=\"90\" src=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-28.png\" alt=\"image\" class=\"wp-image-3369\" title=\"NCERT Class 9 Maths End-of-Chapter (The World of Numbers) Solutions\" srcset=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-28.png 743w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-28-300x36.png 300w\" sizes=\"(max-width: 743px) 100vw, 743px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"683\" src=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-31-1024x683.png\" alt=\"image\" class=\"wp-image-3372\" title=\"NCERT Class 9 Maths End-of-Chapter (The World of Numbers) Solutions\" srcset=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-31-1024x683.png 1024w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-31-300x200.png 300w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-31-768x512.png 768w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-31.png 1536w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<p class=\"has-x-large-font-size wp-block-paragraph\"><strong>Question 13<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"761\" height=\"203\" src=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-29.png\" alt=\"image\" class=\"wp-image-3370\" title=\"NCERT Class 9 Maths End-of-Chapter (The World of Numbers) Solutions\" srcset=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-29.png 761w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-29-300x80.png 300w\" sizes=\"(max-width: 761px) 100vw, 761px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"683\" src=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-32-1024x683.png\" alt=\"image\" class=\"wp-image-3373\" title=\"NCERT Class 9 Maths End-of-Chapter (The World of Numbers) Solutions\" srcset=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-32-1024x683.png 1024w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-32-300x200.png 300w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-32-768x512.png 768w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-32.png 1536w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<p class=\"has-x-large-font-size wp-block-paragraph\"><strong>Question 14<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"760\" height=\"98\" src=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-33.png\" alt=\"image\" class=\"wp-image-3375\" title=\"NCERT Class 9 Maths End-of-Chapter (The World of Numbers) Solutions\" srcset=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-33.png 760w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-33-300x39.png 300w\" sizes=\"(max-width: 760px) 100vw, 760px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"683\" src=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-35-1024x683.png\" alt=\"image\" class=\"wp-image-3378\" title=\"NCERT Class 9 Maths End-of-Chapter (The World of Numbers) Solutions\" srcset=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-35-1024x683.png 1024w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-35-300x200.png 300w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-35-768x512.png 768w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-35.png 1536w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<h1 class=\"wp-block-heading\"><strong>Question 1<\/strong>5<\/h1>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"747\" height=\"74\" src=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-34.png\" alt=\"image\" class=\"wp-image-3377\" title=\"NCERT Class 9 Maths End-of-Chapter (The World of Numbers) Solutions\" srcset=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-34.png 747w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-34-300x30.png 300w\" sizes=\"(max-width: 747px) 100vw, 747px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"683\" src=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-37-1024x683.png\" alt=\"image\" class=\"wp-image-3380\" title=\"NCERT Class 9 Maths End-of-Chapter (The World of Numbers) Solutions\" srcset=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-37-1024x683.png 1024w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-37-300x200.png 300w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-37-768x512.png 768w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-37.png 1536w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<p class=\"has-x-large-font-size wp-block-paragraph\"><strong>Question 16<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"745\" height=\"528\" src=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-36.png\" alt=\"image\" class=\"wp-image-3379\" title=\"NCERT Class 9 Maths End-of-Chapter (The World of Numbers) Solutions\" srcset=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-36.png 745w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-36-300x213.png 300w\" sizes=\"(max-width: 745px) 100vw, 745px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"683\" src=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-38-1024x683.png\" alt=\"image\" class=\"wp-image-3381\" title=\"NCERT Class 9 Maths End-of-Chapter (The World of Numbers) Solutions\" srcset=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-38-1024x683.png 1024w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-38-300x200.png 300w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-38-768x512.png 768w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-38.png 1536w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<h1 class=\"wp-block-heading\">Common Mistakes<\/h1>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Forgetting to simplify fractions.<\/li>\n\n\n\n<li>Confusing repeating decimals with irrational numbers.<\/li>\n\n\n\n<li>Writing \u221a5 as a rational number.<\/li>\n\n\n\n<li>Incorrect placement of decimals on the number line.<\/li>\n\n\n\n<li>Missing the lowest form while converting decimals into fractions.<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h1 class=\"wp-block-heading\">Exam Tips<\/h1>\n\n\n\n<p class=\"wp-block-paragraph\">\u2705 Reduce every fraction to its simplest form.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u2705 Check denominator factors before deciding whether a decimal terminates.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u2705 Use proof by contradiction for irrationality proofs.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u2705 Draw neat number lines with equal intervals.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u2705 For finding rational numbers between two fractions, first make their denominators equal.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h1 class=\"wp-block-heading\">Practice MCQs<\/h1>\n\n\n\n<h3 class=\"wp-block-heading\">1. Which of the following is a terminating decimal?<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">A. 2\/9<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">B. 3\/50<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">C. 5\/12<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">D. 7\/18<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Answer:<\/strong> B<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">2. \u221a5 is:<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">A. Natural<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">B. Rational<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">C. Irrational<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">D. Integer<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Answer:<\/strong> C<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">3. 2.125 in fraction form is:<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">A. 15\/8<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">B. 17\/8<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">C. 19\/8<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">D. 21\/8<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Answer:<\/strong> B<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">4. 3.3 lies between:<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">A. 2 and 3<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">B. 3 and 4<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">C. 4 and 5<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">D. 1 and 2<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Answer:<\/strong> B<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">5. Which is a rational number between 2\/5 and 3\/5?<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">A. 13\/30<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">B. 19\/30<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">C. 1\/5<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">D. 4\/5<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Answer:<\/strong> A<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h1 class=\"wp-block-heading\">FAQ Section<\/h1>\n\n\n\n<h3 class=\"wp-block-heading\">Q1. What is a rational number?<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">A number that can be written as p\/q, where q \u2260 0.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Q2. What is an irrational number?<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">A number that cannot be expressed as p\/q.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Q3. Is every terminating decimal rational?<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Yes.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Q4. Can a repeating decimal be rational?<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Yes. Every repeating decimal is rational.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Q5. Why is \u221a5 irrational?<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Because assuming it to be rational leads to a contradiction.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p class=\"wp-block-paragraph\">Want complete Chapter-wise NCERT Solutions, Mock Tests, Practice Questions, and Exam Preparation Resources?<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Visit <strong><a href=\"http:\/\/www.mymockmate.com\/\">www.mymockmate.com<\/a><\/strong> and boost your preparation with expertly designed study materials and All India Mock Tests.<\/p>\n<div class=\"pdfprnt-buttons pdfprnt-buttons-post pdfprnt-top-bottom-right\"><a href=\"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/posts\/3345?print=print\" class=\"pdfprnt-button pdfprnt-button-print\" target=\"_blank\" ><img decoding=\"async\" src=\"https:\/\/mymockmate.com\/notes\/wp-content\/plugins\/pdf-print\/images\/print.png\" alt=\"image_print\" title=\"Print Content\" \/><span class=\"pdfprnt-button-title pdfprnt-button-print-title\">Print<\/span><\/a> <span class=\"pdfprnt-count-generation\"><\/span><\/div>\n    <div class=\"xs_social_share_widget xs_share_url after_content \t\tmain_content  wslu-style-1 wslu-share-box-shaped wslu-fill-colored wslu-none wslu-share-horizontal wslu-theme-font-no wslu-main_content\">\n\n\t\t\n        <ul>\n\t\t\t        <\/ul>\n    <\/div> \n","protected":false},"excerpt":{"rendered":"<p> Short Introduction The End-of-Chapter Exercises of Chapter 3 &#8220;The World of Numbers&#8221; help students strengthen their understanding<\/p>\n","protected":false},"author":1,"featured_media":3346,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_surecart_dashboard_logo_width":"180px","_surecart_dashboard_show_logo":true,"_surecart_dashboard_navigation_orders":true,"_surecart_dashboard_navigation_invoices":true,"_surecart_dashboard_navigation_subscriptions":true,"_surecart_dashboard_navigation_downloads":true,"_surecart_dashboard_navigation_billing":true,"_surecart_dashboard_navigation_account":true,"postBodyCss":"","postBodyMargin":[],"postBodyPadding":[],"postBodyBackground":{"backgroundType":"classic","gradient":""},"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":true,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2}},"categories":[22,4,11],"tags":[],"class_list":["post-3345","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-cbse","category-class-9","category-maths-class-9"],"jetpack_publicize_connections":[],"_links":{"self":[{"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/posts\/3345","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/comments?post=3345"}],"version-history":[{"count":6,"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/posts\/3345\/revisions"}],"predecessor-version":[{"id":3382,"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/posts\/3345\/revisions\/3382"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/media\/3346"}],"wp:attachment":[{"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/media?parent=3345"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/categories?post=3345"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/tags?post=3345"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}