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[\/et_pb_text][et_pb_text admin_label=”Text” _builder_version=”4.13.1″ _module_preset=”default” text_font_size=”16px” header_2_font=”|600|||||||” header_2_text_color=”#a01414″ header_3_font=”|600|||||||” custom_padding=”15px|15px|54px|4px|false|false” global_colors_info=”{}”]<\/p>\n
In this article, we are going to learn about different types of numbers with the help of examples and learn how to identify them.<\/p>\n
<\/span><\/p>\n Based on the number system, the numbers are classified into six types.<\/strong><\/b><\/p>\n All the positive counting numbers starting from 1 till infinity are known as natural numbers.<\/span><\/p>\n Representation of a set of natural numbers is done by the letter \u201cN\u201d.<\/span><\/p>\n N = {1, 2, 3, 4, 5, 6, ……}<\/span><\/p>\n <\/span><\/p>\n All the natural numbers along with 0 are known as whole numbers.\u00a0<\/span><\/p>\n Representation of a set of whole numbers is done by the letter \u201cW\u201d.<\/span><\/p>\n W = {0, 1, 2, 3, 4, 5, 6, ……}<\/span><\/p>\n <\/span><\/p>\n Zero and positive numbers along with negative numbers are known as Integers.<\/span><\/p>\n Representation of a set of integers is done by the letter \u201cZ\u201d.<\/span><\/p>\n Z = {….., (-3), (-2), (-1), 0, 1, 2, 3, ……}<\/span><\/p>\n <\/span><\/p>\n All the numbers that can be written in the form of \\frac{a}{b}<\/span><\/span>\u00a0are known as rational numbers.<\/span><\/p>\n Where:<\/span><\/p>\n Representation of a set of rational numbers is done by the letter \u201cQ\u201d.<\/span><\/p>\n The decimal expansion of these numbers can be of two types.<\/span><\/p>\n Examples:<\/span><\/p>\n \\frac{1}{2}, \\frac{3}{4}, \\frac{2}{1}, \\frac{-1}{3}, \\frac{8}{9}, \\frac{17}{2}<\/span> and so on.<\/span><\/p>\n <\/p>\n All the numbers which can not be written in the form of \\frac{a}{b}<\/span> <\/span>are known as irrational numbers.\u00a0<\/span><\/p>\n Where,\u00a0<\/span><\/p>\n The decimal expansion of these numbers is always non-terminating and non-recurring.<\/span><\/p>\n Examples:<\/span><\/p>\n \\sqrt{2}, \\sqrt{3}, \\sqrt{5},-\\sqrt{7}<\/span> and so on.<\/span><\/p>\n <\/span><\/p>\n The group of rational numbers and irrational numbers are known as real numbers.<\/span><\/p>\n All types of numbers mentioned above are real numbers.<\/span><\/p>\n Representation of a set of real numbers is done by the letter \u201cR\u201d<\/span><\/p>\n Examples:<\/span><\/p>\n \\sqrt{5},-\\sqrt{7}, \\frac{2}{1}, \\frac{-1}{3}, 0,6,8<\/span>and so on.<\/span><\/p>\n <\/span><\/p>\n <\/span><\/p>\n Based on the divisibility by 2, numbers are classified into two types.<\/strong><\/p>\n These numbers are exactly divisible by 2 and end with 0, 2, 4, 6 and 8.<\/span><\/p>\n Examples:<\/span><\/p>\n 2, 4, 10, 20 and so on.<\/span><\/p>\n <\/span><\/p>\n These numbers are not divisible by 2.<\/span><\/p>\n Examples:<\/span><\/p>\n 1, 9, 11, 27 and so on.<\/span><\/p>\n <\/span><\/p>\n <\/span><\/p>\n Based on the number of factors, numbers are classified into two types.<\/strong>\u00a0<\/p>\n These numbers have only two factors i.e., 1 and the number itself.<\/span><\/p>\n Examples:<\/span><\/p>\n 2, 3, 5, 11, 23 and so on.<\/span><\/p>\n <\/span><\/p>\n These numbers have more than two factors.<\/span><\/p>\n Examples:<\/span><\/p>\n 6, 8, 14, 24 and so on.<\/span><\/p>\n <\/span><\/p>\n 1. Find eight rational numbers having a value more than 6 but less than 7.<\/b><\/p>\n Solution:<\/b><\/b><\/p>\n First, 6 and 7 are written in the form of \\frac{a}{b}<\/span> <\/span>and b = 8 + 1 = 9<\/span><\/p>\n6=\\frac{6 \\times 9}{9}=\\frac{54}{9} <\/span>\n <\/p>\n7=\\frac{7 \\times 9}{9}=\\frac{63}{9}<\/span>\n The eight rational numbers between 6 and 7 are \\frac{55}{9}, \\frac{56}{9}, \\frac{57}{9}, \\frac{58}{9}, \\frac{59}{9}, \\frac{60}{9}, \\frac{61}{9} \\text { and } \\frac{62}{9}<\/span>.<\/span><\/p>\n <\/span><\/p>\n 2. Show that 5 . \\overline{3}<\/span> <\/b>is a rational number.<\/b><\/p>\n Solution:<\/b><\/p>\n Assume that x=5. \\overline{3}<\/span><\/p>\n 100 x=533 . \\overline{3} <\/span> 100 x-10 x=533 . \\overline{3}-53 . \\overline{3}=480 <\/span> Since x can be represented in the form of a fraction, it is rational in nature.<\/span><\/p>\n [\/et_pb_text][\/et_pb_column][et_pb_column type=”2_5″ module_id=”stickysideR” admin_label=”Column R” _builder_version=”4.10.4″ _module_preset=”default” background_color=”#fdefe0″ custom_padding=”25px|25px|25px|25px|true|true” sticky_position=”top” sticky_offset_top=”-280px” sticky_limit_top=”row” sticky_limit_bottom=”row” sticky_position_tablet=”none” sticky_position_phone=”none” sticky_position_last_edited=”on|desktop” sticky_limit_bottom_tablet=”” sticky_limit_bottom_phone=”” sticky_limit_bottom_last_edited=”on|phone” border_radii=”on|15px|15px|15px|15px” box_shadow_style=”preset3″ global_colors_info=”{}”][et_pb_image src=”https:\/\/eistudymaterial.s3.amazonaws.com\/1080×1080.png” alt=”Free Trial banner” title_text=”Mindspark Free Trial Banner” url=”https:\/\/mindspark.in\/free-trial” align=”center” module_class=”adsimg” _builder_version=”4.11.1″ _module_preset=”default” custom_padding=”||||false|false” border_radii=”on|10px|10px|10px|10px” global_colors_info=”{}” transform_styles__hover_enabled=”on|hover” transform_scale__hover_enabled=”on|hover” transform_translate__hover_enabled=”on|desktop” transform_rotate__hover_enabled=”on|desktop” transform_skew__hover_enabled=”on|desktop” transform_origin__hover_enabled=”on|desktop” transform_scale__hover=”102%|102%”][\/et_pb_image][et_pb_text admin_label=”Explore Other Topics [\/et_pb_text][et_pb_text _builder_version=”4.10.7″ _module_preset=”default” text_line_height=”2.2em” link_font_size=”16px” custom_margin=”||0px||false|false” custom_padding=”10px|15px|10px|28px|true|false” locked=”off” global_colors_info=”{}”]<\/p>\n [\/et_pb_text][et_pb_text admin_label=”Related Concepts [\/et_pb_text][et_pb_text _builder_version=”4.13.1″ _module_preset=”default” text_line_height=”2.2em” link_font_size=”16px” custom_margin=”||0px||false|false” custom_padding=”10px|15px|10px|28px|true|false” locked=”off” global_colors_info=”{}”]<\/p>\n [\/et_pb_text][\/et_pb_column][\/et_pb_row][et_pb_row admin_label=”Row for space” _builder_version=”4.10.6″ _module_preset=”default” locked=”off” global_colors_info=”{}”][et_pb_column type=”4_4″ _builder_version=”4.9.11″ _module_preset=”default” global_colors_info=”{}”][et_pb_divider show_divider=”off” _builder_version=”4.10.4″ _module_preset=”default” global_colors_info=”{}”][\/et_pb_divider][\/et_pb_column][\/et_pb_row][\/et_pb_section][et_pb_section fb_built=”1″ admin_label=”banner and faq Section” module_class=”mainsec2″ _builder_version=”4.10.4″ _module_preset=”default” custom_padding=”40px||0px||false|false” global_colors_info=”{}”][et_pb_row use_custom_gutter=”on” gutter_width=”1″ make_equal=”on” disabled_on=”on|on|off” admin_label=”banner Row” _builder_version=”4.10.4″ _module_preset=”default” background_color=”#fff7d6″ width=”100%” max_width=”1310px” height=”134px” custom_margin=”||50px||false|false” custom_padding=”12px||12px||true|false” border_radii=”on|11px|11px|11px|11px” locked=”off” collapsed=”off” global_colors_info=”{}”][et_pb_column type=”4_4″ _builder_version=”4.9.10″ _module_preset=”default” global_colors_info=”{}”][et_pb_image src=”https:\/\/stgwebsite.mindspark.in\/wordpress\/wp-content\/uploads\/2021\/08\/calloutImage.png” title_text=”calloutImage” show_bottom_space=”off” admin_label=”Image” module_class=”img1″ _builder_version=”4.10.8″ _module_preset=”default” width=”25px” height=”60px” custom_padding=”2px||2px||true|false” global_colors_info=”{}”][\/et_pb_image][et_pb_text module_class=”ftstyle” _builder_version=”4.9.10″ _module_preset=”default” text_orientation=”center” global_colors_info=”{}”]<\/p>\n1. Natural numbers\u00a0<\/b><\/h3>\n
2. Whole numbers\u00a0<\/b><\/h3>\n
3. Integers<\/b><\/h3>\n
4. Rational numbers<\/b><\/h3>\n
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5. Irrational numbers<\/b><\/b><\/h3>\n
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6. Real numbers<\/b><\/h3>\n
1. Even numbers<\/b><\/h3>\n
2. Odd numbers<\/b><\/h3>\n
1. Prime numbers\u00a0<\/b><\/b><\/h3>\n
2. Composite numbers<\/b><\/h3>\n
Solved Examples<\/b><\/b><\/h2>\n
10 x=53 . \\overline{3} <\/span><\/p>\n
\\Rightarrow 90 x=480<\/span><\/p>\n\\Rightarrow x=\\frac{480}{90}=\\frac{16}{3}<\/span>\n
\n” _builder_version=”4.9.11″ _module_preset=”default” header_font=”|700|||||||” header_font_size=”25px” text_orientation=”center” custom_margin=”0px||0px||true|false” custom_padding=”8px|15px|0px|15px|false|true” locked=”off” global_colors_info=”{}”]<\/p>\nExplore Other Topics<\/h1>\n
\n” _builder_version=”4.9.11″ _module_preset=”default” header_font=”|700|||||||” header_font_size=”25px” text_orientation=”center” custom_margin=”0px||0px||true|false” custom_padding=”8px|15px|0px|15px|false|true” locked=”off” global_colors_info=”{}”]<\/p>\nRelated Concepts<\/h1>\n