{"id":1958,"date":"2026-05-23T11:01:25","date_gmt":"2026-05-23T11:01:25","guid":{"rendered":"https:\/\/mymockmate.com\/notes\/?p=1958"},"modified":"2026-05-23T11:01:29","modified_gmt":"2026-05-23T11:01:29","slug":"ncert-class-8-maths-a-story-of-numbers-solutions-guide","status":"publish","type":"post","link":"https:\/\/mymockmate.com\/notes\/ncert-class-8-maths-a-story-of-numbers-solutions-guide\/","title":{"rendered":"NCERT Class 8  Maths A Story of Numbers Solutions Guide"},"content":{"rendered":"\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h1 class=\"wp-block-heading\">Short Introduction<\/h1>\n\n\n\n<p class=\"wp-block-paragraph\">The chapter <strong>\u201cA Story of Numbers\u201d<\/strong> explains the fascinating history and evolution of number systems from ancient civilizations to the modern Hindu-Arabic number system. Students learn about Roman numerals, Egyptian numerals, Mesopotamian systems, place value systems, bases, and the importance of zero in mathematics.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h1 class=\"wp-block-heading\">Quick Information Box<\/h1>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><thead><tr><th>Particular<\/th><th>Details<\/th><\/tr><\/thead><tbody><tr><td>Chapter Name<\/td><td>A Story of Numbers<\/td><\/tr><tr><td>Class<\/td><td>Grade 8<\/td><\/tr><tr><td>Subject<\/td><td>Mathematics<\/td><\/tr><tr><td>Main Topics<\/td><td>Number Systems, Roman Numerals, Bases<\/td><\/tr><tr><td>Difficulty Level<\/td><td>Moderate<\/td><\/tr><tr><td>Important For<\/td><td>School Exams, Olympiads<\/td><\/tr><tr><td>Key Skills<\/td><td>Logical Thinking, Number Representation<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\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>Evolution of Numbers<\/li>\n\n\n\n<li>Hindu-Arabic Numerals<\/li>\n\n\n\n<li>Roman Numerals<\/li>\n\n\n\n<li>Egyptian Number System<\/li>\n\n\n\n<li>Mesopotamian Number System<\/li>\n\n\n\n<li>Base Number Systems<\/li>\n\n\n\n<li>Decimal System<\/li>\n\n\n\n<li>Place Value System<\/li>\n\n\n\n<li>Tally Marks<\/li>\n\n\n\n<li>Landmark Numbers<\/li>\n\n\n\n<li>Powers of Numbers<\/li>\n\n\n\n<li>Placeholder Symbol (Zero)<\/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\">Important Formulas<\/h1>\n\n\n\n<h2 class=\"wp-block-heading\">Powers in Base System<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msup><mi>n<\/mi><mn>0<\/mn><\/msup><mo>=<\/mo><mn>1<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">n^0=1<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msup><mi>n<\/mi><mn>1<\/mn><\/msup><mo>=<\/mo><mi>n<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">n^1=n<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msup><mi>n<\/mi><mn>2<\/mn><\/msup><mo>=<\/mo><mi>n<\/mi><mo>\u00d7<\/mo><mi>n<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">n^2=n\\times n<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">Decimal Place Value<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mo stretchy=\"false\">(<\/mo><mi>a<\/mi><mo>\u00d7<\/mo><msup><mn>10<\/mn><mn>3<\/mn><\/msup><mo stretchy=\"false\">)<\/mo><mo>+<\/mo><mo stretchy=\"false\">(<\/mo><mi>b<\/mi><mo>\u00d7<\/mo><msup><mn>10<\/mn><mn>2<\/mn><\/msup><mo stretchy=\"false\">)<\/mo><mo>+<\/mo><mo stretchy=\"false\">(<\/mo><mi>c<\/mi><mo>\u00d7<\/mo><msup><mn>10<\/mn><mn>1<\/mn><\/msup><mo stretchy=\"false\">)<\/mo><mo>+<\/mo><mo stretchy=\"false\">(<\/mo><mi>d<\/mi><mo>\u00d7<\/mo><msup><mn>10<\/mn><mn>0<\/mn><\/msup><mo stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">(a\\times10^3)+(b\\times10^2)+(c\\times10^1)+(d\\times10^0)<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">Base-n Landmark Numbers<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mn>1<\/mn><mo separator=\"true\">,<\/mo><mi>n<\/mi><mo separator=\"true\">,<\/mo><msup><mi>n<\/mi><mn>2<\/mn><\/msup><mo separator=\"true\">,<\/mo><msup><mi>n<\/mi><mn>3<\/mn><\/msup><mo separator=\"true\">,<\/mo><mo>\u22ef<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">1,n,n^2,n^3,\\cdots<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h1 class=\"wp-block-heading\">Questions &amp; Step-by-Step Solutions<\/h1>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h1 class=\"wp-block-heading\">Figure It Out \u2013 Page 54<\/h1>\n\n\n\n<h2 class=\"wp-block-heading\">Q1. Give methods for adding, subtracting, multiplying and dividing using sticks.<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">Solution<\/h3>\n\n\n\n<h3 class=\"wp-block-heading\">Addition<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Combine both groups of sticks together.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Subtraction<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Remove sticks of the smaller group from the larger group.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Multiplication<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Create repeated groups.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Example:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">3 \u00d7 4 means 4 sticks repeated 3 times.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Division<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Distribute sticks equally into groups.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Final Answer<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Arithmetic can be performed by grouping and separating sticks systematically.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">Q2. Extend the letter-based number system.<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">Solution<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">After z:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>aa = 27<\/li>\n\n\n\n<li>ab = 28<\/li>\n\n\n\n<li>ac = 29<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">and so on.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Final Answer<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Using combinations of letters extends the counting system infinitely.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">Q3. Make your own number system.<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">Solution<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Example:<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><thead><tr><th>Number<\/th><th>Symbol<\/th><\/tr><\/thead><tbody><tr><td>1<\/td><td>\u25cf<\/td><\/tr><tr><td>2<\/td><td>\u25cf\u25cf<\/td><\/tr><tr><td>3<\/td><td>\u25b2<\/td><\/tr><tr><td>4<\/td><td>\u25b2\u25cf<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<h3 class=\"wp-block-heading\">Final Answer<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Students may create their own symbols and rules.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h1 class=\"wp-block-heading\">Figure It Out \u2013 Page 59<\/h1>\n\n\n\n<h2 class=\"wp-block-heading\">Q1. Represent the following in Roman numerals<\/h2>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">(i) 1222<\/h3>\n\n\n\n<h3 class=\"wp-block-heading\">Solution<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">1222 = 1000 + 100 + 100 + 10 + 10 + 1 + 1<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Roman numeral:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">MCCXXII<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Final Answer<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">MCCXXII<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">(ii) 2999<\/h3>\n\n\n\n<h3 class=\"wp-block-heading\">Solution<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">2999 = 2000 + 900 + 90 + 9<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Roman numeral:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">MMCMXCIX<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Final Answer<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">MMCMXCIX<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">(iii) 302<\/h3>\n\n\n\n<h3 class=\"wp-block-heading\">Solution<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">302 = 300 + 2<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Roman numeral:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">CCCII<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Final Answer<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">CCCII<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">(iv) 715<\/h3>\n\n\n\n<h3 class=\"wp-block-heading\">Solution<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">715 = 700 + 10 + 5<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Roman numeral:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">DCCXV<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Final Answer<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">DCCXV<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h1 class=\"wp-block-heading\">Figure It Out \u2013 Page 60<\/h1>\n\n\n\n<h2 class=\"wp-block-heading\">Q1. Why do Pacific island people use different number sequences for different objects?<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">Solution<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Different objects may be grouped differently for easier counting and cultural practices.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Final Answer<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Different counting systems improve convenience for specific objects.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">Q2. Evaluate in Gumulgal System<\/h2>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">(i)<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">(ukasar-ukasar-ukasar-ukasar-urapon)<br>+<br>(ukasar-ukasar-ukasar-urapon)<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Solution<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">9 + 7 = 16<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Final Answer<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Equivalent to 16.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">(ii)<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">9 \u2212 6<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Final Answer<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">3<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">(iii)<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">9 \u00d7 4<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Final Answer<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">36<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">(iv)<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">16 \u00f7 4<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Final Answer<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">4<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">Q3. Features of Hindu Number System<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">Solution<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Uses place value<\/li>\n\n\n\n<li>Uses only 10 symbols<\/li>\n\n\n\n<li>Includes zero<\/li>\n\n\n\n<li>Easy arithmetic operations<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Final Answer<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">The Hindu number system is highly efficient and flexible.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h1 class=\"wp-block-heading\">Figure It Out \u2013 Page 62<\/h1>\n\n\n\n<h2 class=\"wp-block-heading\">Q1. Represent in Egyptian System<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">(i) 10458<\/h3>\n\n\n\n<h3 class=\"wp-block-heading\">Solution<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">10458 = 10000 + 400 + 50 + 8<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Represent using Egyptian symbols.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">(ii) 1023<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">1023 = 1000 + 20 + 3<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">(iii) 2660<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">2660 = 2000 + 600 + 60<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">(iv) 784<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">784 = 700 + 80 + 4<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">(v) 1111<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">1111 = 1000 + 100 + 10 + 1<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">(vi) 70707<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">70707 = 70000 + 700 + 7<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h1 class=\"wp-block-heading\">Figure It Out \u2013 Page 63<\/h1>\n\n\n\n<h2 class=\"wp-block-heading\">Q1. Write numbers in Base-5 System<\/h2>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">(i) 15<\/h3>\n\n\n\n<h3 class=\"wp-block-heading\">Solution<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mn>15<\/mn><mo>=<\/mo><mn>3<\/mn><mo>\u00d7<\/mo><mn>5<\/mn><mo>+<\/mo><mn>0<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">15=3\\times5+0<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Final Answer<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">30\u2085<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">(ii) 50<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mn>50<\/mn><mo>=<\/mo><mn>2<\/mn><mo>\u00d7<\/mo><mn>25<\/mn><mo>+<\/mo><mn>0<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">50=2\\times25+0<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Final Answer<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">200\u2085<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">(iii) 137<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mn>137<\/mn><mo>=<\/mo><mn>1<\/mn><mo>\u00d7<\/mo><mn>125<\/mn><mo>+<\/mo><mn>0<\/mn><mo>\u00d7<\/mo><mn>25<\/mn><mo>+<\/mo><mn>2<\/mn><mo>\u00d7<\/mo><mn>5<\/mn><mo>+<\/mo><mn>2<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">137=1\\times125+0\\times25+2\\times5+2<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Final Answer<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">1022\u2085<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">Q2. Can every number be represented?<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">Solution<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Yes. Any number can be expressed using powers of 5.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Final Answer<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Yes, all numbers can be represented.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">Q3. Landmark numbers in Base-7<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">Solution<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mn>1<\/mn><mo separator=\"true\">,<\/mo><mn>7<\/mn><mo separator=\"true\">,<\/mo><mn>49<\/mn><mo separator=\"true\">,<\/mo><mn>343<\/mn><mo separator=\"true\">,<\/mo><mn>2401<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">1,7,49,343,2401<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Final Answer<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">1, 7, 49, 343, 2401 \u2026<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h1 class=\"wp-block-heading\">Figure It Out \u2013 Page 65<\/h1>\n\n\n\n<h2 class=\"wp-block-heading\">Q1. Add Egyptian Numerals<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">Solution<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Group similar symbols together.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Whenever 10 similar symbols occur, replace them with the next higher symbol.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Final Answer<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Egyptian addition is based on regrouping symbols.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">Q2. Add Base-5 Numerals<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">Solution<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Whenever 5 similar symbols occur, regroup into next landmark number.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Final Answer<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Addition works similarly to carrying in decimal system.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h1 class=\"wp-block-heading\">Figure It Out \u2013 Page 69<\/h1>\n\n\n\n<h2 class=\"wp-block-heading\">Q1. Can a symbol appear 10 or more times?<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">Solution<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">No.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">10 repeated symbols are replaced by the next higher symbol.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Final Answer<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">No, regrouping prevents repetition beyond 9.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">Q2. Create Base-4 System<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">Solution<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Landmark numbers:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mn>1<\/mn><mo separator=\"true\">,<\/mo><mn>4<\/mn><mo separator=\"true\">,<\/mo><mn>16<\/mn><mo separator=\"true\">,<\/mo><mn>64<\/mn><mo separator=\"true\">,<\/mo><mn>256<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">1,4,16,64,256<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Representations:<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><thead><tr><th>Decimal<\/th><th>Base-4<\/th><\/tr><\/thead><tbody><tr><td>1<\/td><td>1<\/td><\/tr><tr><td>2<\/td><td>2<\/td><\/tr><tr><td>3<\/td><td>3<\/td><\/tr><tr><td>4<\/td><td>10<\/td><\/tr><tr><td>5<\/td><td>11<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">Q3. Rule for multiplying by 5 in Base-5<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">Solution<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Appending zero shifts to next power.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Example:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mn>23<\/mn><mn>5<\/mn><\/msub><mo>\u00d7<\/mo><mn>5<\/mn><mo>=<\/mo><msub><mn>230<\/mn><mn>5<\/mn><\/msub><\/mrow><annotation encoding=\"application\/x-tex\">23_5\\times5=230_5<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Final Answer<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Add one zero at the end.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h1 class=\"wp-block-heading\">Figure It Out \u2013 Page 73<\/h1>\n\n\n\n<h2 class=\"wp-block-heading\">Q1. Represent in Mesopotamian System<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">(i) 63<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mn>63<\/mn><mo>=<\/mo><mn>1<\/mn><mo>\u00d7<\/mo><mn>60<\/mn><mo>+<\/mo><mn>3<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">63=1\\times60+3<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Final Answer<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">1 sixty and 3 ones.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">(ii) 132<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mn>132<\/mn><mo>=<\/mo><mn>2<\/mn><mo>\u00d7<\/mo><mn>60<\/mn><mo>+<\/mo><mn>12<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">132=2\\times60+12<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Final Answer<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">2 sixties and 12 ones.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">(iii) 200<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mn>200<\/mn><mo>=<\/mo><mn>3<\/mn><mo>\u00d7<\/mo><mn>60<\/mn><mo>+<\/mo><mn>20<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">200=3\\times60+20<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Final Answer<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">3 sixties and 20 ones.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">(iv) 60<\/h3>\n\n\n\n<h3 class=\"wp-block-heading\">Final Answer<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">1 sixty.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">(v) 3605<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mn>3605<\/mn><mo>=<\/mo><mn>1<\/mn><mo>\u00d7<\/mo><mn>3600<\/mn><mo>+<\/mo><mn>5<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">3605=1\\times3600+5<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Final Answer<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">1 three-thousand-six-hundred and 5 ones.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h1 class=\"wp-block-heading\">Common Mistakes<\/h1>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Confusing Roman numerals with Hindu numerals<\/li>\n\n\n\n<li>Forgetting regrouping rules in base systems<\/li>\n\n\n\n<li>Wrong place value interpretation<\/li>\n\n\n\n<li>Ignoring zero as placeholder<\/li>\n\n\n\n<li>Incorrect base conversions<\/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<ul class=\"wp-block-list\">\n<li>Memorise Roman numeral symbols<\/li>\n\n\n\n<li>Practice base conversions regularly<\/li>\n\n\n\n<li>Understand landmark numbers clearly<\/li>\n\n\n\n<li>Learn place value carefully<\/li>\n\n\n\n<li>Revise ancient number systems visually<\/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\">Practice MCQs<\/h1>\n\n\n\n<h2 class=\"wp-block-heading\">1. Which symbol represents 100 in Roman numerals?<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">A. X<br>B. L<br>C. C<br>D. D<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Answer<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">C. C<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">2. Which civilization developed the decimal system?<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">A. Roman<br>B. Egyptian<br>C. Indian<br>D. Greek<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Answer<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">C. Indian<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">3. Which number system uses place value?<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">A. Roman<br>B. Tally Marks<br>C. Hindu-Arabic<br>D. Stick System<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Answer<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">C. Hindu-Arabic<\/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<h2 class=\"wp-block-heading\">Q1. What is a positional number system?<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">A number system where digit position determines value.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">Q2. Why is zero important?<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">It acts as a placeholder in place value systems.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">Q3. What are Roman numerals?<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Ancient numerals used in Rome using symbols like I, V, X, L, C, D, M.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">Q4. What is a base-n system?<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mn>1<\/mn><mo separator=\"true\">,<\/mo><mi>n<\/mi><mo separator=\"true\">,<\/mo><msup><mi>n<\/mi><mn>2<\/mn><\/msup><mo separator=\"true\">,<\/mo><msup><mi>n<\/mi><mn>3<\/mn><\/msup><mo separator=\"true\">,<\/mo><mo>\u22ef<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">1,n,n^2,n^3,\\cdots<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">A system based on powers of n.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">Q5. What is the decimal system?<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">A base-10 number system.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h1 class=\"wp-block-heading\">CTA (Call To Action)<\/h1>\n\n\n\n<p class=\"wp-block-paragraph\">\ud83d\udcd8 Get complete NCERT Solutions, Mock Tests, Practice Questions, and Exam Preparation Resources at:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong><a>www.mymockmate.com<\/a><\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\ud83d\ude80 Practice smarter with All India Mock Tests and Instant Results.<\/p>\n\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 chapter \u201cA Story of Numbers\u201d explains the fascinating history and evolution of number systems from<\/p>\n","protected":false},"author":1,"featured_media":1959,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_angie_page":false,"_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":""},"page_builder":"","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":[122,119,105],"tags":[498,515,512,506,458,457,499,507,502,511,465,470,504,508,509,464,503,494,500,514,477,513,505,510,501,463],"class_list":["post-1958","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-a-story-of-numbers","category-class-8","category-maths-class-8","tag-a-story-of-numbers","tag-ancient-number-systems","tag-base-5-system","tag-base-number-system","tag-cbse-maths-solutions","tag-class-8-mathematics","tag-class-8-maths-solutions","tag-decimal-system","tag-egyptian-number-system","tag-egyptian-numerals","tag-exam-preparation","tag-grade-8-maths","tag-hindu-arabic-numerals","tag-history-of-numbers","tag-maths-chapter-3","tag-maths-mcqs","tag-mesopotamian-numbers","tag-ncert-maths-guide","tag-ncert-solutions-class-8","tag-number-representation","tag-number-system","tag-place-value-questions","tag-place-value-system","tag-roman-number-questions","tag-roman-numerals","tag-step-by-step-solutions"],"jetpack_publicize_connections":[],"_links":{"self":[{"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/posts\/1958","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=1958"}],"version-history":[{"count":1,"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/posts\/1958\/revisions"}],"predecessor-version":[{"id":1960,"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/posts\/1958\/revisions\/1960"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/media\/1959"}],"wp:attachment":[{"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/media?parent=1958"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/categories?post=1958"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/tags?post=1958"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}