{"id":36117,"date":"2023-11-15T19:10:00","date_gmt":"2023-11-15T19:10:00","guid":{"rendered":"https:\/\/www.splashlearn.com\/math-vocabulary\/?page_id=36117"},"modified":"2023-11-20T07:15:39","modified_gmt":"2023-11-20T07:15:39","slug":"representation-of-irrational-numbers-on-number-line-examples-faqs","status":"publish","type":"post","link":"https:\/\/www.splashlearn.com\/math-vocabulary\/representation-of-irrational-numbers-on-number-line","title":{"rendered":"Representation of Irrational Numbers on Number Line &#8211; Examples, FAQs"},"content":{"rendered":"<div class=\"aioseo-breadcrumbs\"><span class=\"aioseo-breadcrumb\">\n\tMath-Vocabulary\n<\/span><\/div>\n\n<div class=\"ub_table-of-contents\" data-showtext=\"show\" data-hidetext=\"hide\" data-scrolltype=\"auto\" id=\"ub_table-of-contents-03ded579-f37f-4f3d-96fc-1fbf451e8b22\" data-initiallyhideonmobile=\"false\"\n                    data-initiallyshow=\"true\"><div class=\"ub_table-of-contents-extra-container\"><div class=\"ub_table-of-contents-container ub_table-of-contents-1-column \"><ul><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/representation-of-irrational-numbers-on-number-line#0-what-is-representation-of-irrational-numbers-on-a-number-line>What Is Representation of Irrational Numbers on a Number Line?<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/representation-of-irrational-numbers-on-number-line#1-what-are-irrational-numbers>What Are Irrational Numbers?<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/representation-of-irrational-numbers-on-number-line#3-how-to-represent-irrational-numbers-on-a-number-line>How to Represent Irrational Numbers on a Number Line<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/representation-of-irrational-numbers-on-number-line#6-solved-examples-on-representation-of-irrational-numbers-on-a-number-line>Solved Examples on Representation of Irrational Numbers on a Number Line<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/representation-of-irrational-numbers-on-number-line#7-practice-problems-on-representation-of-irrational-numbers-on-a-number-line>Practice Problems on Representation of Irrational Numbers on a Number Line<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/representation-of-irrational-numbers-on-number-line#8-frequently-asked-questions-about-representation-of-irrational-numbers-on-a-number-line>Frequently Asked Questions about Representation of Irrational Numbers on a Number Line<\/a><\/li><\/ul><\/div><\/div><\/div>\n\n\n<h2 class=\"wp-block-heading\" id=\"0-what-is-representation-of-irrational-numbers-on-a-number-line\">What Is Representation of Irrational Numbers on a Number Line?<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Representation of irrational numbers can be done by using the Pythagorean theorem. We break down the number inside the square root into two equal parts, where each part represents the side of the <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/right-triangle\">right triangle<\/a> that we form. The hypotenuse of the right triangle represents the given irrational number. This length is used to mark the approximate location of the irrational number on the number line.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"531\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/irrational-numbers-on-number-line-understanding-the-basics.png\" alt=\"Irrational numbers on number line - understanding the basics\" class=\"wp-image-36124\" title=\"Irrational numbers on number line - understanding the basics\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/irrational-numbers-on-number-line-understanding-the-basics.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/irrational-numbers-on-number-line-understanding-the-basics-300x257.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Alt tag: Irrational numbers on number line &#8211; understanding the basics<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Each and every point on a <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/number-sense\/number-line\">number line <\/a>represents a unique real number. We can represent each real number with the help of a unique point on the number line. Irrational numbers and rational numbers together form the set of real numbers.<\/p>\n\n\n\n<div id=\"recommended-games-container-id\" class=\"recommended-games-container\"><h4 class=\"recommended-games-container-headline\">Recommended Games<\/h4><div class=\"recommended-games-container-slides\"><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/10-and-100-more-than-the-same-number\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/add_sub_pv_1_10_100_more_same_num_pt.png\" alt=\"10 and 100 More than the Same Number Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">10 and 100 More than the Same Number Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/add-1-digit-numbers\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/add_sub_facts_add_make_10_pt.png\" alt=\"Add 1-Digit Numbers Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Add 1-Digit Numbers Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/add-10-to-a-3-digit-number\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/add_sub_pv_add_10_number_pt.png\" alt=\"Add 10 to a 3-Digit Number Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Add 10 to a 3-Digit Number Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/add-100-to-a-3-digit-number\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/add_sub_pv_add_100_horizontal_pt.png\" alt=\"Add 100 to a 3-Digit Number Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Add 100 to a 3-Digit Number Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/add-2-digit-and-1-digit-numbers\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/add_sub_pv_add_2d_1d_match_pt.png\" alt=\"Add 2-Digit and 1-Digit Numbers Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Add 2-Digit and 1-Digit Numbers Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/add-2-digit-numbers-by-regrouping\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/add_sub_pv_add_regrp_2d_2d_vertical_pt.png\" alt=\"Add 2-Digit Numbers By Regrouping Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Add 2-Digit Numbers By Regrouping Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/add-3-numbers\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/add_sub_facts_add_3_no_pt.png\" alt=\"Add 3 Numbers Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Add 3 Numbers Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/add-3-numbers-in-any-order\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/add_sub_facts_shifty_bridges_4_gm.png\" alt=\"Add 3 Numbers in Any Order Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Add 3 Numbers in Any Order Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/add-3-numbers-using-groups-of-objects\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/add_sub_facts_add_using_model_pt.png\" alt=\"Add 3 Numbers Using Groups of Objects Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Add 3 Numbers Using Groups of Objects Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/add-3-numbers-using-model\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/add_sub_facts_add_3_no_using_models_pt.png\" alt=\"Add 3 Numbers using Model Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Add 3 Numbers using Model Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><\/div><p class=\"recommended-games-container-desc\"><a href=\"https:\/\/www.splashlearn.com\/games\">More Games<\/a><\/p><button class=\"scroll-right-arrow\"><\/button><\/div><script type=\"text\/javascript\">\n        document.addEventListener(\"DOMContentLoaded\", function() {\n            const container = document.querySelector(\"#recommended-games-container-id\");\n            const slidesContainer = container.querySelector(\".recommended-games-container-slides\");\n            const cards = slidesContainer.querySelectorAll(\".game-card-container-outer\");\n            const scrollRightArrow = container.querySelector(\".scroll-right-arrow\");\n\n            function adjustContainerStyles() {\n                const numCards = cards.length;\n\n                if (numCards === 1) {\n                    container.style.maxWidth = \"30%\";\n                    container.style.textAlign = \"center\";\n                } else if (numCards === 2) {\n                    container.style.maxWidth = \"50%\";\n                    container.style.textAlign = \"center\";\n                } else if (numCards === 3) {\n                    container.style.maxWidth = \"75%\";\n                    container.style.textAlign = \"center\";\n                } else {\n                    container.style.maxWidth = \"\";\n                    container.style.textAlign = \"\";\n                }\n            }\n\n            function checkScrollPosition() {\n                const maxScrollLeft = slidesContainer.scrollWidth - slidesContainer.clientWidth;\n                if ((slidesContainer.scrollLeft + 10) >= maxScrollLeft) {\n                    scrollRightArrow.style.display = \"none\"; \/\/ Hide the arrow if fully scrolled\n                } else {\n                    scrollRightArrow.style.display = \"block\"; \/\/ Show the arrow if not fully scrolled\n                }\n            }\n\n            scrollRightArrow.addEventListener(\"click\", function() {\n                const scrollAmount = 300; \/\/ Adjust based on the container's width and your needs\n                slidesContainer.scrollLeft += scrollAmount;\n                setTimeout(checkScrollPosition, 100); \/\/ Delay to allow scroll update\n            });\n\n            adjustContainerStyles();\n            checkScrollPosition();\n            slidesContainer.addEventListener(\"scroll\", checkScrollPosition);\n        });\n    <\/script><h2 class=\"wp-block-heading\" id=\"1-what-are-irrational-numbers\">What Are Irrational Numbers?<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\"><a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/number\/irrational-numbers#:~:text=An%20irrational%20number%20is%20a,and%20interactive%20for%20all%20students.\">I<strong>rrational numbers<\/strong><\/a><strong> are the real numbers that cannot be written in the form of a ratio (rational form) <\/strong>$\\frac{p}{q}$<strong>, where p, q are integers and <\/strong>$q \\neq 0$<strong>.<\/strong>&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">In simple words, all the real numbers that are not <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/rational-numbers\">rational numbers<\/a> are irrational. These numbers include non-terminating, non-repeating decimals.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"661\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/rational-and-irrational-numbers.png\" alt=\"Rational and irrational numbers\" class=\"wp-image-36125\" title=\"Rational and irrational numbers\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/rational-and-irrational-numbers.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/rational-and-irrational-numbers-281x300.png 281w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<div id=\"recommended-worksheets-container-id\" class=\"recommended-games-container\"><h4 class=\"recommended-games-container-headline\">Recommended Worksheets<\/h4><div class=\"recommended-games-container-slides\"><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/1-and-2-more-within-10-horizontal-addition\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/1-and-2-more-within-10-horizontal-addition.jpeg\" alt=\"1 and 2 more within 10: Horizontal Addition Worksheet\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/1-and-2-more-within-10-vertical-addition\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/1-and-2-more-within-10-vertical-addition.jpeg\" alt=\"1 and 2 more within 10: Vertical Addition Worksheet\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/1-and-2-more-within-20-horizontal-addition\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/1-and-2-more-within-20-horizontal-addition.jpeg\" alt=\"1 and 2 more within 20: Horizontal Addition Worksheet\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/1-and-2-more-within-20-vertical-addition\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/1-and-2-more-within-20-vertical-addition.jpeg\" alt=\"1 and 2 more within 20: Vertical Addition Worksheet\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/10-and-100-more-than-a-3-digit-number\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/10-and-100-more-than-a-3-digit-number.jpeg\" alt=\"10 and 100 More than a 3-digit Number\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/100-more-and-100-less-than-a-3-digit-number\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/100-more-and-100-less-than-a-3-digit-number.jpeg\" alt=\"100 More and 100 Less than a 3-digit Number\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/100-more-than-a-3-digit-number\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/100-more-than-a-3-digit-number.jpeg\" alt=\"100 More than a 3-digit Number\">\r\n\t    <\/div>\r\n\t\t<div 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src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/add-1-digit-and-3-digit-numbers-and-match-the-sum.jpeg\" alt=\"Add 1 Digit and 3 Digit Numbers and Match the Sum\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><\/div><p class=\"recommended-games-container-desc\"><a href=\"https:\/\/www.splashlearn.com\/worksheets\">More Worksheets<\/a><\/p><button class=\"scroll-right-arrow\"><\/button><\/div><script type=\"text\/javascript\">\n        document.addEventListener(\"DOMContentLoaded\", function() {\n            const container = document.querySelector(\"#recommended-worksheets-container-id\");\n            const slidesContainer = container.querySelector(\".recommended-games-container-slides\");\n            const cards = slidesContainer.querySelectorAll(\".worksheet-card-container-outer\");\n            const scrollRightArrow = container.querySelector(\".scroll-right-arrow\");\n\n            function adjustContainerStyles() {\n                const numCards = cards.length;\n\n                if (numCards === 1) {\n                    container.style.maxWidth = \"30%\";\n                    container.style.textAlign = \"center\";\n                } else if (numCards === 2) {\n                    container.style.maxWidth = \"50%\";\n                    container.style.textAlign = \"center\";\n                } else if (numCards === 3) {\n                    container.style.maxWidth = \"75%\";\n                    container.style.textAlign = \"center\";\n                } else {\n                    container.style.maxWidth = \"\";\n                    container.style.textAlign = \"\";\n                }\n            }\n\n            function checkScrollPosition() {\n                const maxScrollLeft = slidesContainer.scrollWidth - slidesContainer.clientWidth;\n                if ((slidesContainer.scrollLeft + 10) >= maxScrollLeft) {\n                    scrollRightArrow.style.display = \"none\"; \/\/ Hide the arrow if fully scrolled\n                } else {\n                    scrollRightArrow.style.display = \"block\"; \/\/ Show the arrow if not fully scrolled\n                }\n            }\n\n            scrollRightArrow.addEventListener(\"click\", function() {\n                const scrollAmount = 300; \/\/ Adjust based on the container's width and your needs\n                slidesContainer.scrollLeft += scrollAmount;\n                setTimeout(checkScrollPosition, 100); \/\/ Delay to allow scroll update\n            });\n\n            adjustContainerStyles();\n            checkScrollPosition();\n            slidesContainer.addEventListener(\"scroll\", checkScrollPosition);\n        });\n    <\/script><h2 class=\"wp-block-heading\" id=\"2-what-is-a-number-line\">What Is a Number Line?<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>In math, a number line is a pictorial representation of numbers on a straight line (horizontally or vertically).&nbsp;<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The numbers on a number line are placed sequentially at equal distances along its length.&nbsp;<\/li>\n\n\n\n<li>It can be extended infinitely in both directions and is usually represented horizontally.&nbsp;<\/li>\n<\/ul>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Writing numbers on the number line makes it easier to compare numbers or to perform arithmetic operations on them.&nbsp;<\/li>\n\n\n\n<li>Numbers on the right side of 0 are positive. Numbers on the left side of 0 are negative.<\/li>\n\n\n\n<li>The numbers on a number line increase as one moves from left to right and decrease on moving from right to left.&nbsp;<\/li>\n<\/ul>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"533\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/number-line.png\" alt=\"Number line\" class=\"wp-image-36126\" title=\"Number line\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/number-line.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/number-line-300x258.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"3-how-to-represent-irrational-numbers-on-a-number-line\">How to Represent Irrational Numbers on a Number Line<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Irrational numbers in the form of $\\sqrt{n}$, where n is a positive integer can be represented on a number line. Keep in mind that irrational numbers cannot be represented precisely on a number line due to their infinite and non-repeating decimal expansions, so we use approximations to visually represent them.&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Let\u2019s see the steps to represent irrational numbers on a number line.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Steps Used to Represent Irrational Numbers on a Number Line<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Let\u2019s understand the steps with the help of an example.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Example: Represent <\/strong>$\\sqrt{2}$<strong> on a number line<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Step 1:<\/strong> Draw a number line. Mark and label integers 0, 1, and -1 as shown below.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"458\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/representing-2-on-a-number-line-step-i.png\" alt=\"Representing 2 on a number line - step i\" class=\"wp-image-36127\" title=\"Representing 2 on a number line - step i\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/representing-2-on-a-number-line-step-i.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/representing-2-on-a-number-line-step-i-300x222.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Step 2:<\/strong> We can express $\\sqrt{2}$<strong> as <\/strong>$\\sqrt{2} = \\sqrt{1 + 1}$<strong>.<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Let the point representing zero be O.&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Let the point representing 1 be B.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Draw a line perpendicular at B such that <em>l<\/em>(AB)=1 unit.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Step 3:<\/strong> Construct a right-angled triangle OAB by joining OA.&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">AB will be the height, OB will be the base, and OA will be the hypotenuse.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"478\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/representing-2-on-a-number-line-step-ii.png\" alt=\"Representing 2 on a number line - step ii\" class=\"wp-image-36128\" title=\"Representing 2 on a number line - step ii\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/representing-2-on-a-number-line-step-ii.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/representing-2-on-a-number-line-step-ii-300x231.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Step 4: <\/strong>Find the length of the hypotenuse by applying the Pythagorean Theorem<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$(OA)^{2} = (AB)^{2} + (BC)^{2}$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$(OA)^{2} = (1)^{2} + (1)^{2}$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$(OA)^{2} = &nbsp; 2$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$OA&nbsp; = \\sqrt{2}$<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"478\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/representing-2-on-a-number-line-step-iii.png\" alt=\"Representing 2 on a number line - step iii\" class=\"wp-image-36129\" title=\"Representing 2 on a number line - step iii\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/representing-2-on-a-number-line-step-iii.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/representing-2-on-a-number-line-step-iii-300x231.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Step 5: <\/strong>Now, keeping OA as radius and O as the center, draw an arc on the number line and name the point as P. Now, the distance OP is equal to $\\sqrt{2}$. The<strong> <\/strong>point P represents $\\sqrt{2}$ on the number line.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"468\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/representation-of-2-on-the-number-line-step-iv.png\" alt=\"Representation of 2 on the number line - step iv\" class=\"wp-image-36130\" title=\"Representation of 2 on the number line - step iv\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/representation-of-2-on-the-number-line-step-iv.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/representation-of-2-on-the-number-line-step-iv-300x226.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"4-facts-about-representation-of-irrational-numbers-on-a-number-line\">Facts about Representation of Irrational Numbers on a Number Line<\/h2>\n\n\n\n<div style=\"color:#0369a1;background-color:#e0f2fe\" class=\"wp-block-roelmagdaleno-callout-block has-text-color has-background is-layout-flex wp-container-roelmagdaleno-callout-block-is-layout-4fc3f8e1 wp-block-roelmagdaleno-callout-block-is-layout-flex\"><div>\n<ul class=\"wp-block-list\">\n<li>Rational numbers are countable but the real numbers are uncountable. Irrational numbers are all those real numbers that aren&#8217;t rational. Irrationals make up all the remaining, uncountable real numbers.&nbsp;<\/li>\n\n\n\n<li>(\u200b\u200bpi) is the ratio of the circumference of a circle to its diameter. Its decimal representation is non-terminating and non-repeating. It is an irrational number (a transcendental to be more specific). It is not a root of any non-zero polynomial of finite degree with rational coefficients.<\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"5-conclusion\">Conclusion<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">In this article, we have learned about irrational numbers and how they can be represented on the number line. Irrational numbers are special in a way that though they cannot be expressed fully as fractions, they can be visualized on a number line by using approximations. Now let&#8217;s solve some examples and practice problems to understand the concept in a better way!<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"6-solved-examples-on-representation-of-irrational-numbers-on-a-number-line\">Solved Examples on Representation of Irrational Numbers on a Number Line<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Example 1: Represent <\/strong><strong>5<\/strong><strong> on the number line.<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Step 1:<\/strong> Draw a number line and mark the points 0, 1, and -1.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"421\" height=\"55\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/a-number-line.png\" alt=\"A number line\" class=\"wp-image-36131\" title=\"A number line\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/a-number-line.png 421w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/a-number-line-300x39.png 300w\" sizes=\"auto, (max-width: 421px) 100vw, 421px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Step 2:<\/strong> Draw a line perpendicular at the point 1 in such a way that the perpendicular line segment has a length of 2 units.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Step 3:<\/strong> Construct a right-angled triangle ABC as shown below. AB will be the height, BC will be the base, and AC will be the hypotenuse.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"424\" height=\"266\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/constructing-ABC-from-the-point-0-on-the-number-line.png\" alt=\"constructing ABC from the point 0 on the number line\" class=\"wp-image-36132\" title=\"constructing ABC from the point 0 on the number line\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/constructing-ABC-from-the-point-0-on-the-number-line.png 424w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/constructing-ABC-from-the-point-0-on-the-number-line-300x188.png 300w\" sizes=\"auto, (max-width: 424px) 100vw, 424px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Step 4: <\/strong>Find the length of the hypotenuse by applying the Pythagorean Theorem<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$(AC)^{2} = (AB)^{2} + (BC)^{2}$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$(AC)^{2} = (2)^{2} + (1)^{2}$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$(AC)^{2} =&nbsp; 4 + 1$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$AC = \\sqrt{5}$<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"424\" height=\"266\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/finding-length-AC-using-pythagorean-theorem.png\" alt=\"Finding length AC using pythagorean theorem\" class=\"wp-image-36133\" title=\"Finding length AC using pythagorean theorem\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/finding-length-AC-using-pythagorean-theorem.png 424w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/finding-length-AC-using-pythagorean-theorem-300x188.png 300w\" sizes=\"auto, (max-width: 424px) 100vw, 424px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Step 5:<\/strong> Now with AC as radius and C as the center, draw an arc on the number line that cuts the number line at D. Here, CD will represent the distance $\\sqrt{5}$.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Thus, the point D represents $\\sqrt{5}$ on the number line.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"424\" height=\"266\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/representing-5-on-the-number-line.png\" alt=\"Representing 5 on the number line\" class=\"wp-image-36134\" title=\"Representing 5 on the number line\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/representing-5-on-the-number-line.png 424w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/representing-5-on-the-number-line-300x188.png 300w\" sizes=\"auto, (max-width: 424px) 100vw, 424px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Example 2: Represent <\/strong><strong>3<\/strong><strong> on the number line.<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Solution:&nbsp;<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">In order to represent $\\sqrt{3}$ on the number line, we must first represent $\\sqrt{2}$&nbsp; on the number line. We have already discussed the steps for representing $\\sqrt{2}$.<strong> <\/strong>Suppose, we mark $\\sqrt{2}$<strong> <\/strong>on the number line as shown below using point P.&nbsp;&nbsp;<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"540\" height=\"124\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/square-root-2-on-number-line.png\" alt=\"Square root 2 on number line\" class=\"wp-image-36135\" title=\"Square root 2 on number line\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/square-root-2-on-number-line.png 540w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/square-root-2-on-number-line-300x69.png 300w\" sizes=\"auto, (max-width: 540px) 100vw, 540px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Now, we will use this point P to locate $\\sqrt{3}$ on the number line. Take base $= OP = \\sqrt{2}$<strong> <\/strong>units. Draw a perpendicular at P of 1 unit length. Using pythagoras theorem, we get<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Hypotenuse $= (\\sqrt{2})^{2} + (1)^{2} = \\sqrt{2 + 1} = \\sqrt{3}$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Taking origin as center and hypotenuse as radius, draw an arc that meets the number line at point M.&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The point M represents the irrational number $\\sqrt{3}$ on the number line.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"549\" height=\"124\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/square-root-3-on-number-line.png\" alt=\"Square root 3 on number line\" class=\"wp-image-36136\" title=\"Square root 3 on number line\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/square-root-3-on-number-line.png 549w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/square-root-3-on-number-line-300x68.png 300w\" sizes=\"auto, (max-width: 549px) 100vw, 549px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Example 3: Represent <\/strong>$\\sqrt{7}$<strong> on the number line.<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Solution:&nbsp;<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"437\" height=\"356\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/7-on-the-number-line.png\" alt=\"7 on the number line\" class=\"wp-image-36137\" title=\"7 on the number line\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/7-on-the-number-line.png 437w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/7-on-the-number-line-300x244.png 300w\" sizes=\"auto, (max-width: 437px) 100vw, 437px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">i) We can use $\\sqrt{5}$ and $\\sqrt{6}$ to represent $\\sqrt{7}$ on the number line.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Here, $\\sqrt{5} = \\sqrt{2^{2} + 1^{1}}$ can be represented by applying Pythagoras theorem in a right triangle with base = 2 units and height 1 unit.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Suppose that the point L represents $\\sqrt{5}$.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">ii) Next, we can express $\\sqrt{6} = \\sqrt{(\\sqrt{5})^{2} + 1^{1}}$.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">To represent $\\sqrt{6}$, choose base length $= OL = \\sqrt{5}$ units and height = 1 unit. Let point M represent $\\sqrt{6}$ on the number line.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">iii) Similarly, we can write $\\sqrt{7} = \\sqrt{(\\sqrt{6})^{2} + 1^{1}}$.&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">To represent $\\sqrt{7}$, choose base = OM = 6 units and height = 1 unit. Draw an arc keeping 0 as center and hypotenuse OZ as radius. Suppose it meets the number line at point N.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Here, OZ = ON = $\\sqrt{7}$.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The point N represents $\\sqrt{7}$.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"7-practice-problems-on-representation-of-irrational-numbers-on-a-number-line\">Practice Problems on Representation of Irrational Numbers on a Number Line<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\"><div class=\"spq_wrapper\"><h2 style=\"display:none;\">Representation of Irrational Numbers on Number Line - Examples, FAQs<\/h2><p style=\"display:none;\">Attend this quiz & Test your knowledge.<\/p><div class=\"spq_question_wrapper\" data-answer=\"1\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">1<\/span><h3 class=\"sqp_question_text\">$\\sqrt{5}$ is _______<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">a rational number.<\/div><div class=\"spq_answer_block\" data-value=\"1\">an irrational number.<\/div><div class=\"spq_answer_block\" data-value=\"2\">an integer.<\/div><div class=\"spq_answer_block\" data-value=\"3\">a fraction.<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: an irrational number.<br\/>$\\sqrt{5}$ is an irrational number since it is not a rational number. It cannot be written in the form $\\frac{p}{q}$, where p, q are integers and $q \\neq 0$.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"2\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">2<\/span><h3 class=\"sqp_question_text\">Which of the following right triangles will be used to represent $\\sqrt{13}$?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">Base = 10, height = 3<\/div><div class=\"spq_answer_block\" data-value=\"1\">Base = 9, height = 4<\/div><div class=\"spq_answer_block\" data-value=\"2\">Base = 3, height = 2<\/div><div class=\"spq_answer_block\" data-value=\"3\">Base = 3, height = 3<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: Base = 3, height = 2<br\/>$\\sqrt{13} = \\sqrt{9 + 4} = \\sqrt{3^{2} + 2^{2}}$<br>\r\nThus, the hypotenuse will be $\\sqrt{13}$. It can be used to locate $\\sqrt{13}$ on the number line.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"2\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">3<\/span><h3 class=\"sqp_question_text\">If we take base = 3 units and height = 1 unit, we can use the hypotenuse length to represent the irrational number ____ on the number line.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$\\sqrt{2}$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$\\sqrt{7}$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$\\sqrt{10}$<\/div><div class=\"spq_answer_block\" data-value=\"3\">$\\sqrt{5}$<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: $\\sqrt{10}$<br\/>$\\sqrt{3^{2} + 1^{1}} = \\sqrt{10}$<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"3\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">4<\/span><h3 class=\"sqp_question_text\">A number is irrational if and only if its decimal representation is ________.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">terminating<\/div><div class=\"spq_answer_block\" data-value=\"1\">non-terminating and repeating<\/div><div class=\"spq_answer_block\" data-value=\"2\">non-terminating<\/div><div class=\"spq_answer_block\" data-value=\"3\">non-terminating and non-repeating<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: non-terminating and non-repeating<br\/>A number is irrational if and only if its decimal representation is non-terminating and non-repeating.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"0\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">5<\/span><h3 class=\"sqp_question_text\">Every point on a number line represents a unique_________.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">real number<\/div><div class=\"spq_answer_block\" data-value=\"1\">natural number<\/div><div class=\"spq_answer_block\" data-value=\"2\">irrational number<\/div><div class=\"spq_answer_block\" data-value=\"3\">rational number<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: real number<br\/>Every point on a number line represents a unique real number.<\/span><\/div><\/div><\/div><\/div>  <script type=\"application\/ld+json\">{\n        \"@context\": \"https:\/\/schema.org\/\", \n        \"@type\": \"Quiz\", \n        \"typicalAgeRange\": \"3-11\",\n        \"educationalLevel\":  \"beginner\",\n        \"assesses\" : \"Attend this quiz & Test your knowledge.\",\n        \"educationalAlignment\": [\n              {\n                \"@type\": \"AlignmentObject\",\n                \"alignmentType\": \"educationalSubject\",\n                \"targetName\": \"Math\"\n              }] ,\n        \"name\": \"Representation of Irrational Numbers on Number Line - Examples, FAQs\",        \n        \"about\": {\n                \"@type\": \"Thing\",\n                \"name\": \"Representation of Irrational Numbers on Number Line\"\n        },  \n        \"hasPart\": [{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"$$\\\\sqrt{5}$$ is _______\",\n                    \"text\": \"$$\\\\sqrt{5}$$ is _______\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"$$\\\\sqrt{5}$$ is an irrational number since it is not a rational number. It cannot be written in the form $$\\\\frac{p}{q}$$, where p, q are integers and $$q \\\\neq 0$$.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"a rational number.\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$\\\\sqrt{5}$$ is an irrational number since it is not a rational number. It cannot be written in the form $$\\\\frac{p}{q}$$, where p, q are integers and $$q \\\\neq 0$$.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"an integer.\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$\\\\sqrt{5}$$ is an irrational number since it is not a rational number. It cannot be written in the form $$\\\\frac{p}{q}$$, where p, q are integers and $$q \\\\neq 0$$.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"a fraction.\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$\\\\sqrt{5}$$ is an irrational number since it is not a rational number. It cannot be written in the form $$\\\\frac{p}{q}$$, where p, q are integers and $$q \\\\neq 0$$.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 1,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"an irrational number.\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"$$\\\\sqrt{5}$$ is an irrational number since it is not a rational number. It cannot be written in the form $$\\\\frac{p}{q}$$, where p, q are integers and $$q \\\\neq 0$$.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"$$\\\\sqrt{5}$$ is an irrational number since it is not a rational number. It cannot be written in the form $$\\\\frac{p}{q}$$, where p, q are integers and $$q \\\\neq 0$$.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Which of the following right triangles will be used to represent $$\\\\sqrt{13}$$?\",\n                    \"text\": \"Which of the following right triangles will be used to represent $$\\\\sqrt{13}$$?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"$$\\\\sqrt{13} = \\\\sqrt{9 + 4} = \\\\sqrt{3^{2} + 2^{2}}$$<br>\r\nThus, the hypotenuse will be $$\\\\sqrt{13}$$. It can be used to locate $$\\\\sqrt{13}$$ on the number line.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"Base = 10, height = 3\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$\\\\sqrt{13} = \\\\sqrt{9 + 4} = \\\\sqrt{3^{2} + 2^{2}}$$<br>\r\nThus, the hypotenuse will be $$\\\\sqrt{13}$$. It can be used to locate $$\\\\sqrt{13}$$ on the number line.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"Base = 9, height = 4\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$\\\\sqrt{13} = \\\\sqrt{9 + 4} = \\\\sqrt{3^{2} + 2^{2}}$$<br>\r\nThus, the hypotenuse will be $$\\\\sqrt{13}$$. It can be used to locate $$\\\\sqrt{13}$$ on the number line.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"Base = 3, height = 3\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$\\\\sqrt{13} = \\\\sqrt{9 + 4} = \\\\sqrt{3^{2} + 2^{2}}$$<br>\r\nThus, the hypotenuse will be $$\\\\sqrt{13}$$. It can be used to locate $$\\\\sqrt{13}$$ on the number line.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 2,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"Base = 3, height = 2\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"$$\\\\sqrt{13} = \\\\sqrt{9 + 4} = \\\\sqrt{3^{2} + 2^{2}}$$<br>\r\nThus, the hypotenuse will be $$\\\\sqrt{13}$$. It can be used to locate $$\\\\sqrt{13}$$ on the number line.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"$$\\\\sqrt{13} = \\\\sqrt{9 + 4} = \\\\sqrt{3^{2} + 2^{2}}$$<br>\r\nThus, the hypotenuse will be $$\\\\sqrt{13}$$. It can be used to locate $$\\\\sqrt{13}$$ on the number line.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"If we take base = 3 units and height = 1 unit, we can use the hypotenuse length to represent the irrational number ____ on the number line.\",\n                    \"text\": \"If we take base = 3 units and height = 1 unit, we can use the hypotenuse length to represent the irrational number ____ on the number line.\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"$$\\\\sqrt{3^{2} + 1^{1}} = \\\\sqrt{10}$$\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\sqrt{2}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$\\\\sqrt{3^{2} + 1^{1}} = \\\\sqrt{10}$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\sqrt{7}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$\\\\sqrt{3^{2} + 1^{1}} = \\\\sqrt{10}$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\sqrt{5}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$\\\\sqrt{3^{2} + 1^{1}} = \\\\sqrt{10}$$\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 2,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$\\\\sqrt{10}$$\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"$$\\\\sqrt{3^{2} + 1^{1}} = \\\\sqrt{10}$$\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"$$\\\\sqrt{3^{2} + 1^{1}} = \\\\sqrt{10}$$\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"A number is irrational if and only if its decimal representation is ________.\",\n                    \"text\": \"A number is irrational if and only if its decimal representation is ________.\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"A number is irrational if and only if its decimal representation is non-terminating and non-repeating.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"terminating\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"A number is irrational if and only if its decimal representation is non-terminating and non-repeating.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"non-terminating and repeating\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"A number is irrational if and only if its decimal representation is non-terminating and non-repeating.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"non-terminating\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"A number is irrational if and only if its decimal representation is non-terminating and non-repeating.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 3,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"non-terminating and non-repeating\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"A number is irrational if and only if its decimal representation is non-terminating and non-repeating.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"A number is irrational if and only if its decimal representation is non-terminating and non-repeating.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Every point on a number line represents a unique_________.\",\n                    \"text\": \"Every point on a number line represents a unique_________.\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"Every point on a number line represents a unique real number.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"natural number\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Every point on a number line represents a unique real number.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"irrational number\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Every point on a number line represents a unique real number.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"rational number\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Every point on a number line represents a unique real number.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 0,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"real number\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"Every point on a number line represents a unique real number.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"Every point on a number line represents a unique real number.\"\n                      }\n                    } \n\n                    }]}<\/script><\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"8-frequently-asked-questions-about-representation-of-irrational-numbers-on-a-number-line\">Frequently Asked Questions about Representation of Irrational Numbers on a Number Line<\/h2>\n\n\n<div class=\"wp-block-ub-content-toggle\" id=\"ub-content-toggle-5b2f6a76-eeaa-4c7a-978e-ae9bca465268\" data-mobilecollapse=\"true\" data-desktopcollapse=\"true\">\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-0-5b2f6a76-eeaa-4c7a-978e-ae9bca465268\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-5b2f6a76-eeaa-4c7a-978e-ae9bca465268\"><strong>How many irrational numbers are there on the number line?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-0-5b2f6a76-eeaa-4c7a-978e-ae9bca465268\">\n\n<p class=\"wp-block-paragraph\">There are an infinite number of irrational numbers.<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-1-5b2f6a76-eeaa-4c7a-978e-ae9bca465268\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-5b2f6a76-eeaa-4c7a-978e-ae9bca465268\"><strong>Are real numbers countable?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-1-5b2f6a76-eeaa-4c7a-978e-ae9bca465268\">\n\n<p class=\"wp-block-paragraph\">No, real numbers are not countable.<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-2-5b2f6a76-eeaa-4c7a-978e-ae9bca465268\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-5b2f6a76-eeaa-4c7a-978e-ae9bca465268\"><strong>Is 1 rational or irrational?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-2-5b2f6a76-eeaa-4c7a-978e-ae9bca465268\">\n\n<p class=\"wp-block-paragraph\">1 is a rational number. It can be written as $\\frac{1}{1}$.<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-3-5b2f6a76-eeaa-4c7a-978e-ae9bca465268\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-5b2f6a76-eeaa-4c7a-978e-ae9bca465268\"><strong>Can irrational numbers be represented on the number line?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-3-5b2f6a76-eeaa-4c7a-978e-ae9bca465268\">\n\n<p class=\"wp-block-paragraph\">Irrational numbers are considered as the subset of real numbers and they can be represented on a number line. However, while representing an irrational number, we represent the approximate value of the number on the number line.<\/p>\n\n<\/div><\/div>\n<\/div>","protected":false},"excerpt":{"rendered":"<p>What Is Representation of Irrational Numbers on a Number Line? Representation of irrational numbers can be done by using the Pythagorean theorem. We break down the number inside the square root into two equal parts, where each part represents the side of the right triangle that we form. The hypotenuse of the right triangle represents &#8230; <a title=\"Representation of Irrational Numbers on Number Line &#8211; Examples, FAQs\" class=\"read-more\" href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/representation-of-irrational-numbers-on-number-line\" aria-label=\"More on Representation of Irrational Numbers on Number Line &#8211; Examples, FAQs\">Read more<\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"ub_ctt_via":"","footnotes":""},"categories":[1],"tags":[],"class_list":["post-36117","post","type-post","status-publish","format-standard","hentry","category-all"],"featured_image_src":null,"author_info":{"display_name":"Mithun Jhawar","author_link":"https:\/\/www.splashlearn.com\/math-vocabulary\/author\/mithun-jhawarsplashlearn-com\/"},"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/36117","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/comments?post=36117"}],"version-history":[{"count":9,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/36117\/revisions"}],"predecessor-version":[{"id":36144,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/36117\/revisions\/36144"}],"wp:attachment":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/media?parent=36117"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/categories?post=36117"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/tags?post=36117"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}