{"id":7563,"date":"2021-10-26T23:05:17","date_gmt":"2021-10-26T17:35:17","guid":{"rendered":"https:\/\/mathemerize.com\/?p=7563"},"modified":"2021-11-27T17:33:52","modified_gmt":"2021-11-27T12:03:52","slug":"what-are-rational-and-irrational-numbers-with-examples","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/what-are-rational-and-irrational-numbers-with-examples\/","title":{"rendered":"What are Rational and Irrational Numbers with Examples ?"},"content":{"rendered":"

Here you will learn what are rational and irrational numbers with examples.<\/p>\n

Let’s begin –<\/p>\n

What are Rational and Irrational Numbers ?<\/h2>\n

Rational Number<\/strong><\/h3>\n

A rational number is defined as number of the form a\/b where a and b are integers and b \\(\\ne\\) 0.<\/p>\n

The set of rational numbers encloses the set of integers and fractions.<\/p>\n

Rational numbers that are not integral will have decimal values. These values can be of two types :<\/p>\n

(a) Terminating (or finite) decimal fractions<\/strong> : For example, 17\/4 = 4.25, 21\/5 = 4.2 and so forth.<\/p>\n

(b) Non-terminating decimal fractions<\/strong> : Amongst non-terminating decimal fractions there are two types of decimal values.<\/p>\n

(i) Non-terminating periodic fractions<\/strong> : These are non-terminating decimal fractions of the type \\(x.a_1a_2….a_na_1a_2….a_n\\). For example \\(16\\over 3\\) = 5.3333, 15.23232323, 14.28762876….  and so on.<\/p>\n

(ii) Non-terminating non-periodic fractions<\/strong> : These are of the form \\(x.b_1b_2….b_nc_1c_2…c_n\\). For example, 5.273168143725186….<\/p>\n

Of the above categories,terminating decimal and non-terminating periodic decimal fractions belong to the set of rational numbers.<\/p>\n

Irrational Number<\/strong><\/h3>\n

Fractions, that are non-terminating, non-periodic fractions are called irrational numbers.<\/p>\n

Some examples of irrational numbers are \\(\\sqrt{2}\\), \\(\\sqrt{3}\\) etc. In other words, all square and cube roots of the natural numbers that are not squares and cubes of natural numbers are irrational. Other irrational numbers include \\(\\pi\\), e and so on.<\/p>\n

Every positive irrational number has a negative irrational number corresponding to it.<\/p>\n

All operations of addition, subtraction, multiplication and division applicable to rational numbers are also applicable to irrational numbers.<\/p>\n

You should realise that once an irrational numbers appears in the solution of question, it can only disappear if it is multiplied or divided by the same irrational number.<\/p>\n\n\n

\n
Next – How to Find Least Common Multiple (LCM) of Numbers and Fractions<\/a><\/div>\n<\/div>\n\n\n\n
\n
Previous – Prime Numbers in Math<\/a><\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

Here you will learn what are rational and irrational numbers with examples. Let’s begin – What are Rational and Irrational Numbers ? Rational Number A rational number is defined as number of the form a\/b where a and b are integers and b \\(\\ne\\) 0. The set of rational numbers encloses the set of integers …<\/p>\n

What are Rational and Irrational Numbers with Examples ?<\/span> Read More »<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"default","ast-global-header-display":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"default","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":""},"categories":[62],"tags":[505,503,504],"yoast_head":"\nWhat are Rational and Irrational Numbers with Examples ?<\/title>\n<meta name=\"description\" content=\"In this post you will learn what are rational and irrational numbers with examples.\" \/>\n<meta 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