{"id":5529,"date":"2013-02-25T01:34:08","date_gmt":"2013-02-25T01:34:08","guid":{"rendered":"http:\/\/SchoolTutoring.com\/help\/?p=5529"},"modified":"2014-12-02T08:27:05","modified_gmt":"2014-12-02T08:27:05","slug":"schooltutoring-com-reviews-rational-irrational-real-and-imaginary-numbers","status":"publish","type":"post","link":"https:\/\/schooltutoring.com\/help\/schooltutoring-com-reviews-rational-irrational-real-and-imaginary-numbers\/","title":{"rendered":"SchoolTutoring.com Reviews Rational, Irrational, Real, and Imaginary Numbers"},"content":{"rendered":"

Overview:\u00a0 Types of Numbers<\/strong><\/p>\n

There are many different ways to describe numbers as they are used in operations and in algebra.\u00a0 When students look at the number line, most numbers on that line are rational.\u00a0 They can be expressed as fractions or as decimals that divide exactly and are terminating. Other numbers (just as real), never do divide exactly into a neat ratio.\u00a0 Still other numbers can be imagined, but they do not have a real solution at all.<\/p>\n

Rational Numbers\u00a0Can Be\u00a0Written as Fractions<\/strong><\/p>\n

Rational numbers include the integers (counting numbers) and all fractions.\u00a0 They are called “rational” because they can be also written as an exact ratio, which is another way of saying that they can be written as a fraction.\u00a0 The fraction will always mean exactly the same thing as the rational number, no matter how many decimal points that are used.\u00a0 Repeating decimals, such as those that were discussed in Fractions to Decimals and Decimals to Fractions are one type of rational number.<\/p>\n

Pi Is an Irrational Number<\/strong><\/p>\n

Irrational numbers are a special type of number that can never be expressed exactly by a fraction.\u00a0 \u00a0\u00a0For example, decimals that do not repeat, such as pi<\/em>, and any square roots that do not come out even, such as the square root of 2 are irrational numbers.\u00a0 No matter how many decimal places that pi<\/em> is calculated to, there’s never a repeating pattern, but it is useful for determining the circumference of a circle.\u00a0 The ancient Greeks used geometric proofs, such as the Pythagorean theorem, to describe the lengths of line segments that were irrational.<\/p>\n

Density of the Number Line and Real Numbers<\/strong><\/p>\n

If all rational numbers are plotted on a number line that stretches out infinitely, the line will be densely populated.\u00a0 One can always find a point that will fall between them, and there is still room between those rational numbers to plot the irrational numbers.\u00a0 Rational and Irrational numbers together form the set of real numbers.\u00a0 All the operations and properties apply to real numbers, so they can be added, subtracted, multiplied, and divided, according to number theory.<\/p>\n

Imaginary Numbers Have Applications<\/strong><\/p>\n

If the number line is expanded to become a number plane, some numbers that are neither rational nor irrational can be plotted.\u00a0 These are “imaginary numbers”\u00a0 which are defined as multiples of the square root of -1.\u00a0 It has no real solution, because the square root of a number is always positive.\u00a0 They have many applications as \u00a0complex numbers in quantum mechanics and fluid dynamics.<\/p>\n

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SchoolTutoring Academy<\/span> is the premier educational services company for K-12 and college students. We offer tutoring programs for students in K-12, AP classes, and college. To learn more about how we help parents and students in Minneapolis, MN visit: Tutoring in Minneapolis, MN<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"

Overview:\u00a0 Types of Numbers There are many different ways to describe numbers as they are used in operations and in algebra.\u00a0 When students look at the number line, most numbers on that line are rational.\u00a0 They can be expressed as fractions or as decimals that divide exactly and are terminating. Other numbers (just as real), […]<\/p>\n","protected":false},"author":22,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"inline_featured_image":false,"footnotes":""},"categories":[2],"tags":[913,985,1220,1485,1498],"class_list":["post-5529","post","type-post","status-publish","format-standard","hentry","category-algebra","tag-imaginary-numbers","tag-irrational-numbers","tag-number-theory","tag-rational-numbers","tag-real-numbers"],"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts\/5529","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/users\/22"}],"replies":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/comments?post=5529"}],"version-history":[{"count":0,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts\/5529\/revisions"}],"wp:attachment":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/media?parent=5529"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/categories?post=5529"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/tags?post=5529"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}