{"id":2399,"date":"2012-07-18T22:45:32","date_gmt":"2012-07-18T22:45:32","guid":{"rendered":"http:\/\/schooltutoring.com\/scholarship\/?p=2399"},"modified":"2014-12-02T08:33:41","modified_gmt":"2014-12-02T08:33:41","slug":"mathematics-different-types-of-numbers","status":"publish","type":"post","link":"https:\/\/schooltutoring.com\/scholarship\/2012\/07\/18\/mathematics-different-types-of-numbers\/","title":{"rendered":"Mathematics: Different Types of Numbers"},"content":{"rendered":"

There are many types of numbers, arranged in sets<\/a> such as Natural numbers, Whole numbers, Integers, Rational numbers, Irrational numbers etc.<\/p>\n

Natural numbers:<\/h4>\n

The set of natural numbers is denoted by N, begins with 1 and contains all the numbers which are used for counting.<\/p>\n

 <\/p>\n

N = {1,2,3,4,5 ,\u2026}<\/p>\n

 <\/p>\n

Whole numbers:<\/h4>\n

The set of whole numbers denoted by\u00a0 W, has all the natural numbers and also a zero.<\/p>\n

 <\/p>\n

W={0,1,2,3,4,\u2026}<\/p>\n

 <\/p>\n

Additive inverse of a natural number:<\/h4>\n

The additive inverse of a number x is \u2013x.<\/p>\n

 <\/p>\n

Example: The additive inverse of 4 is -4<\/p>\n

 <\/p>\n

Note:<\/strong> <\/span><\/p>\n

a)\u00a0\u00a0\u00a0\u00a0\u00a0 The sum of a number and its additive inverse is zero.<\/p>\n

Example: 4+ (-4) =0.<\/p>\n

 <\/p>\n

b)\u00a0\u00a0\u00a0\u00a0\u00a0 The aditive inverse of 0 is 0. Because 0+0=0.<\/p>\n

 <\/p>\n

Integers:<\/h4>\n

The set of integers denoted by\u00a0 Z or I, is the set of all the whole numbers and their additive inverses.<\/p>\n

 <\/p>\n

Z or I = {\u2026, -3, -2, -1, 0, 1, 2, 3,\u2026}<\/p>\n

 <\/p>\n

Rational number:<\/h4>\n

The set of rational numbers denoted by Q contains the numbers of the form p\/q, where p and q are integers and q\u22600.<\/p>\n

 <\/p>\n

Examples:<\/strong><\/p>\n

\"\"<\/a><\/p>\n

Insertion of rational numbers:<\/h4>\n

There exists infinite number of rational numbers between any two real numbers.<\/p>\n

 <\/p>\n

Example:<\/span><\/strong>\u00a0 Find any two rational numbers between 2.1 and 3.5.<\/p>\n

 <\/p>\n

Solution:<\/span><\/strong><\/p>\n

The average of 2 numbers lies between those 2 numbers.<\/p>\n

Average of 2.1 and 3.5= \"\"<\/a><\/p>\n

Average of 2.1 and 2.8 = \"\"<\/a><\/p>\n

So, 2 rational numbers between 2.1 and 3.5 are 2.8 and 2.45.<\/p>\n

 <\/p>\n

Note:<\/span><\/strong><\/p>\n

Similarly we can find infinite number of rational numbers.<\/p>\n

For example, the average of 2.8 and 3.5 also lies between given two numbers,<\/p>\n

The average of 2.45 and 3.5 also lies between given two numbers etc.<\/p>\n

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 Oakley visit: Tutoring in Oakley. <\/a><\/p>\n","protected":false},"excerpt":{"rendered":"

There are many types of numbers, arranged in sets such as Natural numbers, Whole numbers, Integers, Rational numbers, Irrational numbers etc. Natural numbers: The set of natural numbers is denoted by N, begins with 1 and contains all the numbers which are used for counting.   N = {1,2,3,4,5 ,\u2026}   Whole numbers: The set […]<\/p>\n","protected":false},"author":19,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"inline_featured_image":false,"footnotes":""},"categories":[2,11],"tags":[945,984,1179,1223,1484,2571],"class_list":["post-2399","post","type-post","status-publish","format-standard","hentry","category-algebra","category-math-fundamentals","tag-integer","tag-irrational","tag-natural","tag-numbers","tag-rational","tag-whole"],"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts\/2399","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/users\/19"}],"replies":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/comments?post=2399"}],"version-history":[{"count":0,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts\/2399\/revisions"}],"wp:attachment":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/media?parent=2399"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/categories?post=2399"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/tags?post=2399"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}