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Topic: Recurring decimals

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	Decimal - Encyclopedia, History, Geography and Biography
		Decimal notation is the writing of numbers in the base-ten numeral system, which uses various symbols (called digits) for ten distinct values (0, 1, 2, 3, 4, 5, 6, 7, 8 and 9) to represent numbers.
		Decimal fractions are commonly expressed without a denominator, the decimal separator being inserted into the numerator (with leading zeros added if needed), at the position from the right corresponding to the power of ten of the denominator.
		That a rational must produce a finite or recurring decimal expansion can be seen to be a consequence of the long division algorithm, in that there are only (q-1) possible nonzero remainders on division by q, so that the recurring pattern will have a period less than q-1.
	www.arikah.com /encyclopedia/Decimal (1484 words)

	Decimal - ExampleProblems.com
		Decimal notation is the writing of numbers in the base-ten numeral system, which uses various symbols for ten distinct quantities (0, 1, 2, 3, 4, 5, 6, 7, 8 and 9, called digits) to represent numbers.
		Decimal arithmetic is used in computers so that fractional results can be computed exactly, which is not possible using a binary fractional representation.
		Decimal fractions can be expressed without a denominator, the decimal point being inserted into the numerator (with leading zeros added if needed), at the position from the right corresponding to the power of ten of the denominator.
	www.exampleproblems.com /wiki/index.php/Decimal (1138 words)

	Revision Centre - GCSE Maths - Number - Decimals
		A recurring decimal is a decimal number which does go on forever, but some of the digits are repeated over and over again.
		In decimal form, a rational number (fraction) is either an exact or a recurring decimal.
		Sometimes recurring decimals are written with a bar over the digits which are repeated, or with dots over the first and last digits that are repeated.
	www.revisioncentre.co.uk /gcse/maths/decimals.html (437 words)

	Recurring decimal - Wikipedia, the free encyclopedia
		A recurring or repeating decimal is a number which when expressed as a decimal has a set of "final" digits which repeat an infinite number of times.
		More fully: a recurring decimal is a real number whose expression in the (decimal numeral system) has some point after which the same sequence of digits repeats infinitely-many times.
		A decimal number written with a repeating final 0 is NOT classed as a recurring decimal, and the decimal is said to terminate before the first final 0 (because it is not necessary to explicitly write that there is a repeating "0".
	en.wikipedia.org /wiki/Recurring_decimal (1413 words)

	Decimal Summary
		A decimal fraction is a number written in decimal notation that does not have any digits except 0 to the left of the decimal point.
		Decimal is derived from Latin as "decem" (10) and Greek "deka" (10).
		These digits are often used with a decimal separator which indicates the start of a fractional part, and with one of the sign symbols + (plus) or − (minus) to indicate sign.
	www.bookrags.com /Decimal (4114 words)

	Duodecimal Summary
		As explained in recurring decimals, whenever an irreducible fraction is written in “decimal” notation, in any base, the fraction can be expressed exactly (terminates) if and only if all the prime factors of its denominator are also prime factors of the base.
		Thus, in practical applications, the nuisance of recurring decimals is encountered less often when duodecimal notation is used.
		However, when recurring fractions do occur in duodecimal notation, they are less likely to have a very short period than in decimal notation, because 12 (twelve) is between two prime numbers, 11 (eleven) and 13 (thirteen), whereas ten is adjacent to composite number 9.
	www.bookrags.com /Duodecimal (2289 words)

	Decimals
		A decimal number is one that shows parts of a whole one in terms of the number of tenths, hundredths and thousandths it represents.
		Some decimal numbers have an infinite number of decimal places but have digits that repeat, or re occur, in a pattern; these are called 'recurring' decimals.
		For more help with converting decimals into percentages and fractions, or vice versa, see the sub topic ‘Converting Decimals, Fractions and Percentages’ beneath the title for this topic or in the menu to the left of the screen.
	www.roehampton.ac.uk /lskills/TLTP3/WN/NumeracyDecimals.html (1599 words)

	MathsNet: AS/A2 Modular Mathematics Background
		A recurring decimal is one whose digits after the decimal point do not end but repeat the same sequence for ever.
		Recurring decimals are also known as repeating decimals or periodic decimals.
		All fractions can be written either as recurring decimals or as terminating decimals.
	www.mathsnet.net /asa2/2004/backrecur.html (232 words)

	Decimals
		Decimals are the part of the number which come after the decimal point.
		These are decimals which end straight away (1.5, 0.1234, 1.2345).
		These include numbers such as PI or recurring decimals like a third.
	www.projectgcse.co.uk /maths/decimals.htm (102 words)

	Fraction families and decimal relations - Sarah, Ellie, Andrew, Darren and Fiona
		They were then given three fractions to write as decimals and used calculators to explore the relationship between other fractions and decimals.
		Ellie and Andrew, in their game of snap, have related fractions such as 3/10 and 64/100 to their fraction and decimal equivalents, and so are beginning to work within level 4.
		Their work shows they know that to change a fraction to a decimal they must divide the numerator by the denominator.
	www.ncaction.org.uk /search/comment.htm?id=576 (312 words)

	Decimals
		A recurring decimal is a decimal number which does go on forever, but where some of the digits are repeated over and over again.
		Other decimals are those which go on forever and don't have digits which repeat.
		You can tell if a fraction will be an exact or a recurring decimal as follows: fractions with denominators that have only prime factors of 2 and 5 will be exact decimals.
	www.mathsrevision.net /gcse/pages.php?page=8 (576 words)

	Count On
		(a recurring fraction which goes on for ever), mathematicians use one of two common notations to indicate which (if any) of the digits are in the repeating part (also called the period or cycle).
		Numbers whose decimal fraction terminate or end up recurring are proper fractions.
		An example is the square root of 2 whose decimal fraction is 1.41421 35623 73095....
	www.counton.org /explorer/fractions (1898 words)

	Decimal - Wikipedia, the free encyclopedia
		It is the most widely used numeral system, perhaps because humans have four fingers and a thumb on each hand, giving a total of ten digits over both hands.
		The integer part or integral part of a decimal number is the part to the left of the decimal separator (see also floor function).
		The part from the decimal separator to the right is the fractional part; if considered as a separate number, a zero is often written in front.
	en.wikipedia.org /wiki/Decimal (1436 words)

	Patent 2126615
		When any digit is divided by twelve to obtain a decimal fraction, a quotient is obtained which is either correct to a limited number of decimal places or contains a recurring digit after a limited number of decimal places.
		The arrangement is such that each pair of brushes 512 turns through half a revolution for each revolution of the accumulator wheel 589 and comes to rest in position to connect the segment $17 to a segment 514 corresponding to the digit registered by the wheel 519.
		In a decimal accumulator the gear ratio between each gear 517 and the associated accumulator wheel 519 is 14:10 so that the gear wheel 509 turns through one revolution while the wheel 507 is turning through 10/14 of a revolution.
	www.uspto.gov /web/menu/busmethp/2126615.html (3967 words)

	PinkMonkey.com Algebra Study Guide 1.4 Real Numbers
		For decimal representation of p/q, now we have merely to consider the decimal form of fraction r/q which we usually write to the right of the decimal point.
		In case of "non-terminating type" we have decimal fractions having an infinite number of digits.
		In "endless recurring or infinite repeating" decimal fractions we can see that when p is actually divided by q the possible remainders are 1, 2, 3,.....
	www.pinkmonkey.com /studyguides/subjects/algebra/chap1/a0101401.asp (530 words)

	Recurring Decimals
		So far, we have considered divisions with a limited number of decimal places in the quotient (i.e.
		This is an example of a recurring decimal.
		This is written by placing a dot over the first and the last recurring digit.
	www.mathsteacher.com.au /year8/ch02_fracdec/09_recur/dec.htm (192 words)

	Political Crossfire Forums :: View topic - 0.9... = 1 (Site not responding. Last check: 2007-10-13)
		This relies on a very simple technique for transforming recurring decimals into fractions that I learned in school, but never thought to apply to this specific issue.
		Note that a similar situation occurs in different bases, when you multiply by the appropriate base (which I think is the word you were looking for) with the appropriate weird decimal.
		This is why multiplying (or dividing) by a power of 10 will simply move the decimal poing left or right...because 10 is what our number system is based on.
	www.politicalcrossfire.com /forum/viewtopic.php?t=59318 (2917 words)

	Number 142857
		The number 142857 is actually a recurring decimal or also known as circulating number.
		The formation of this number can be understood by taking the reciprocal of the number 7 with which 142857 is very much related.
		Actually various properties are associated with the recurring decimals.
	www.geocities.com /vijaymankar/142857right.htm (391 words)

	Base 24 - Wikipedia, the free encyclopedia
		Decimal Equivalent 10 twenty four 24 24 100 ?
		recur because they include 5 as a factor; ¹⁄
		The multiples of decimal hundred are 44, 88, CC, GG, LL, 110, etc.
	en.wikipedia.org /wiki/Base_24 (324 words)

	Recurring Decimals
		Sometimes when dividing, the division will never stop as there is always a remainder.
		Write the decimal 0.3333… in recurring decimal form.
		Write the decimal 4.27777… in recurring decimal form.
	www.mathsteacher.com.au /year7/ch06_decimals/15_recur/dec.htm (298 words)

	AAEGT template (Site not responding. Last check: 2007-10-13)
		is converted to a decimal the result is 0.11111...
		Note that this means that these are two different names for precisely the same number.
		(a) Look at your conversions of fractions into decimals where the result was a recurring decimal.
	www.tased.edu.au /tasonline/tag/aaegt7/forbes2a.htm (210 words)

	Periodic numbers, 1.9999999 == 2? - GameDev.Net Discussion Forums
		I mean, the idea of repeating decimals is bordering on illogical to begin with.
		A recurring decimal place doesn't actually have any bearing on this problem at all, it just makes the error harder to spot.
		If you now assume that A is 1.999 recurring, it doesn't change the outcome, the zero digit is now just added at infinity plus 1, and keeps the result just under 2.
	www.gamedev.net /community/forums/topic.asp?topic_id=321863 (1683 words)

	Recurring decimals in prime fractions
		is a prime, it is always a recurring decimal with a period
		I was thinking why inverting a prime number should always give a recurring decimal but could not think of a reason other than it has to be something to do with our base 10 system of counting.
		This can't be true either, it will always be finite as 1/pq is a rational number, and hence its decimal either terminates or repeats.
	www.physicsforums.com /showthread.php?t=116215 (1525 words)

	5 - Recurring Decimals (Site not responding. Last check: 2007-10-13)
		The first three are all relatively straightforward, but d) is a much more complicated recurring decimal.
		The number is in fact a decimal approximation to
		You have to be very familiar with decimal approximations to spot this one!
	www.cimt.plymouth.ac.uk /resources/res1/decimals.htm (161 words)

	Algebra
		They include also all integers (3 for example can be put in the form of 3/1).
		When they are written as decimals, the decimals will be terminating or recurring nonterminating decimals.
		Sometimes, they are put in the form of an infinite, but not a recurring decimal.
	library.thinkquest.org /C006002/Pages/algebra.htm (287 words)

	Simple maths but i don't understand why (about recurring decimals or repeating)
		Simple maths but i don't understand why (about recurring decimals or repeating)
		When calculating recurring decimals, we let X to be that number to calculate it for example:
		Search for other threads like this on this forum, there have been a ton of them.
	www.physicsforums.com /showthread.php?t=129166 (1257 words)

	infinity in numbers - FrostCloud Forums
		Assuming we add q (refer to the earlier part of this doc for what q is) to 0, we can then go ahead and add "wholes" ie 0.999...
		I'm not explaining this good am I? you are talking about two different (sets of) numbers here, one is 0.999999...
		The other is 0.99..9 (and numbers like it) that have a finite set of recurring digits.
	www.frostcloud.com /forum/showthread.php?t=1211 (2057 words)

	What's the point? (Site not responding. Last check: 2007-10-13)
		These are decimals which end straight away (
		Many answers you work out may give a long string of decimal places which don't seem to end.
		Questions in an exam may ask you to give answers to a specific degree of accuracy by writing answers to a number of significant figures or to a number of decimal places.
	www.easymaths.com /What's_the_point.htm (127 words)

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