{"id":6179,"date":"2013-07-26T02:23:25","date_gmt":"2013-07-26T02:23:25","guid":{"rendered":"https:\/\/schooltutoring.com\/help\/?p=6179"},"modified":"2014-12-02T08:26:59","modified_gmt":"2014-12-02T08:26:59","slug":"a-review-of-math-fundamentals-place-value","status":"publish","type":"post","link":"https:\/\/schooltutoring.com\/help\/a-review-of-math-fundamentals-place-value\/","title":{"rendered":"A Review of Math Fundamentals: Place Value"},"content":{"rendered":"

Overview:\u00a0 Place Value and Numeration Systems<\/strong>
\nThe earliest representations of numbers were simple tally marks.\u00a0 As long as the numbers involved were not very large, tally marks were sufficient.\u00a0 As soon as larger numbers were necessary to conduct transactions, a system was needed to represent them.\u00a0 These systems involved grouping, with symbols \u00a0to mark the number of groups.\u00a0 For example, the ancient Egyptians used a grouping of tally marks for numbers smaller than 10, a marking similar to a heel bone for 10, a marking like a coiled rope for 100, a marking like a lotus flower for 1000, and so on.\u00a0 The markings for numbers were not random, but followed a certain order from left to right.<\/p>\n

Number Bases<\/strong>
\nMany early number systems were based upon groups of five, for counting on one hand and using another, or groups of ten, such as our system and the ancient Egyptian system among others.\u00a0 A system that is in Base 10 is based upon powers of ten.\u00a0 For example, reading from right to left, our numeration system starts with ones, then 101<\/sup>, 102<\/sup>, 103.<\/sup>, and so on.\u00a0 (100<\/sup> power actually equals 1, by definition, so the system is intact.) The place a digit is located in the particular numeral determines its value.\u00a0 In the number 321, the 3 means something different, 300, than in the number 35.\u00a0 There it means only 30.<\/p>\n

The Zero and Place Value<\/strong>
\nThere was not a separate symbol for zero in many ancient number systems.\u00a0 For example, the ancient Egyptians used only the markings for which they had values, so a number such as 306 would have been represented by three coiled ropes and 6 tally marks.\u00a0 In India, zero was treated like a common number much earlier, but it wasn’t until the Middle Ages that the Arabic system, including the Indian use of zero, was introduced to Europe.\u00a0 Zero as a placeholder is used in place of the blank in many systems.<\/p>\n

Place Value, Decimals, Very Large, and Very Small Numbers<\/strong>
\nIn the discussion of number bases, our decimal system uses exponential values of 10, so that the place value of very large numbers can be represented easily by the number of zeros that are in the number.\u00a0 Similarly, place value can be represented for very small numbers by the number of places following the decimal point.\u00a0 For most uses, only a few decimal places either way are sufficient.<\/p>\n

Scientific Notation\u00a0 and Place Value<\/strong>
\nScientific notation provides an efficient shorthand to denote very large and very small numbers, such as distances in space or the size of microscopic organisms.\u00a0 For example, the average distance from the Sun to Pluto is 3.669 X 109<\/sup> miles, or 3, 669,000,000 miles.\u00a0\u00a0\u00a0 The size of some viruses is 9.14 X 10-7<\/sup> cm or .000000914 cm.\u00a0 It is relatively easy to convert numbers that have many zeroes in them as placeholders to scientific notation by using the rules of place value and the decimal system.<\/p>\n

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Overview:\u00a0 Place Value and Numeration Systems The earliest representations of numbers were simple tally marks.\u00a0 As long as the numbers involved were not very large, tally marks were sufficient.\u00a0 As soon as larger numbers were necessary to conduct transactions, a system was needed to represent them.\u00a0 These systems involved grouping, with symbols \u00a0to mark the […]<\/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":[11],"tags":[1218,1332,1593,2596],"class_list":["post-6179","post","type-post","status-publish","format-standard","hentry","category-math-fundamentals","tag-number-bases","tag-place-value","tag-scientific-notation","tag-zero"],"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts\/6179","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=6179"}],"version-history":[{"count":0,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts\/6179\/revisions"}],"wp:attachment":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/media?parent=6179"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/categories?post=6179"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/tags?post=6179"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}