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	Numbers - Estimating and Rounding - First Glance (Site not responding. Last check: 2007-11-07)
		If that digit is greater than or equal to five, add one to the rounding digit and drop all digits to the right of it.
		If that digit is less than 5, do not change the "rounding digit" but change all digits to the right of the "rounding digit" to zero.
		If that digit is greater than or equal to 5, add one to the rounding digit and change all digits to the right of the rounding digit to zero.
	www.math.com /school/subject1/lessons/S1U1L3GL.html (200 words)

	Rounding Numbers — FactMonster.com
		7.8199 rounded to the nearest tenth is 7.8
		1.0621 rounded to the nearest hundredth is 1.06
		3.8792 rounded to the nearest thousandth is 3.879
	www.factmonster.com /ipka/A0875987.html (557 words)

	Rounding - Wikipedia, the free encyclopedia
		Example: 73 rounded to the nearest ten is 70, because 73 is closer to 70 than to 80.
		This method is sometimes known as "round to even" and is used in order to eliminate the bias that would come from always rounding a number ending in five up every time.
		Other methods of rounding include round towards zero (also known as truncation), round away from zero, floor (reduce non-round numbers to greatest lesser round number) and ceiling (increase non-round numbers to least greater round number).
	en.wikipedia.org /wiki/Rounding (394 words)

	Rounding - Search Results - MSN Encarta (Site not responding. Last check: 2007-11-07)
		Rounding, process for approximating a number to the nearest value, which may be less than or greater than the original number.
		Round (mathematics), to approximate a number by replacing it with a simpler number, one with fewer digits or one with zeros for its ending digits....
		Round, short vocal composition in which all voice parts sing the same melody at the same pitch, but each part enters at a given number of beats...
	encarta.msn.com /Rounding.html (189 words)

	Roundedness - Wikipedia, the free encyclopedia
		In phonetics, vowel roundedness refers to the amount of rounding in the lips during the articulation of a vowel.
		In endolabial rounding, the corners of the mouth are drawn slightly together and the lips may be compressed horizontally, but the lips do not protrude and only their outer surface is exposed.
		In exolabial rounding, the lips protrude like a tube, as when kissing; the inner surface of the lips is exposed.
	en.wikipedia.org /wiki/Rounded_vowel (462 words)

	Article - "Measurement Error Due to Rounding"
		Rounding error is the difference between the true value and the nearest reportable value.
		Rounding is not the only source of measurement error or variation.
		As a rule of thumb, the standard deviation due to rounding is one quarter of the difference between consecutive reportable values.
	www.variation.com /techlib/vr-1.html (467 words)

	Rounding Bottom (Reversal) (Site not responding. Last check: 2007-11-07)
		When the rounding bottom does finally form, its low may not be the lowest low of the last few months.
		However, rounding bottoms represent long-term reversal and this new support level may not be that significant.
		A rounding bottom could be thought of as a head and shoulders bottom without readily identifiable shoulders.
	www.stockcharts.com /education/ChartAnalysis/roundingBottom.html (727 words)

	Rounding Numbers
		Rounding makes numbers that are easier to work with in your head.
		Use rounding to get a answer that is close but that does not have to be exact.
		The number 88 rounded to the nearest ten would be 90.
	www.aaamath.com /est27a-rounding.html (129 words)

	Rounding (Site not responding. Last check: 2007-11-07)
		Rounding is typically resolved when quantization constraints are applied to a computed result in order to satisfy the requirements of the type to which the result is to be assigned.
		Rounding mode to round towards the "nearest neighbor" unless both neighbors are equidistant, in which case, round towards the even neighbor.
		Rounding mode to round towards "nearest neighbor" unless both neighbors are equidistant, in which case round "ceiling".
	chess.eecs.berkeley.edu /ptexternal/src/ptII/doc/codeDoc/ptolemy/math/Rounding.html (1307 words)

	Rounding Error
		Rounding (roundoff) error is a phenomenon of digital computing resulting from the computer's inability to represent some numbers exactly.
		For instance, with rounding, the lost bits in the representation of 1/10 are rounded up, but the lost bits in the representation of 7/10 are rounded down.
		Rounding error is a natural consequence of the representation scheme used for integers and floating-point numbers in digital computers.
	www.mcs.drexel.edu /~introcs/F2K/lectures/5_Scientific/Rounding/index.html (2356 words)

	Adventures In Rounding
		If the call is rounded to 3.1 minutes from 4.0 minutes (four minutes equals forty tenths of a minute), you lose 9 of 40 tenths of a minute you would charge for.
		The impact of rounding is relative to the ratio between your average unrounded value and your maximum rounding amount.
		In the case of telephony with sixty second rounding, the ratio is roughly 3.5 versus 1.0.
	www.servicelevel.net /rating_matters/newsletters/issue01.htm (717 words)

	Etherington & Roberts. Dictionary--rounding (Site not responding. Last check: 2007-11-07)
		Rounding takes place after the spine has been given a light coat of adhesive, and is accomplished by means of light hammering along the spine with a round-headed hammer.
		A book is rounded to help prevent the spine from falling in, i.e., assuming a concave shape (and a convex fore edge), which would result in severe strain on the hinges of the book.
		The practice of rounding the spines of books dates back to at least the middle of the 15th century, and, during the course of years, the "proper" shape of the round has ranged from a nearly flat spine to a highly exaggerated arc.
	palimpsest.stanford.edu /don/dt/dt2916.html (229 words)

	Math Forum - Ask Dr. Math Archives: Rounding Numbers
		If the digit to the right of your rounding digit is less than 5 (0 through 4), round down (drop all digits to the right of the digit you are rounding, replacing them with zeros).
		361 rounded to the nearest 10 is 360, which is a multiple of 10.
		361 rounded to the nearest 100 is 400, which is a multiple of 100.
	www.mathforum.org /library/drmath/sets/select/dm_rounding.html (375 words)

	rounding idea bank
		> rounding to the nearest 10 and 100.
		To introduce rounding to my lower kids, I do a little activity called "In the Neighborhood." I explain that there is a family of grown-ups living in a neighborhood.
		When rounding there are only two options; once that is decided it is easy to pick which number is closer.
	www.mathcats.com /grownupcats/ideabankrounding.html (1385 words)

	Rounding off
		we round up (that is add 1) if the next figure is 5 or more, we round down (that is just drop them) if the next number is less than 5.
		Rounding off to the nearest hundredths is sometimes referred to as rounding off to 2 decimal places.
		Round off to the nearest cent means round off to the nearest hundredths or round off to two decimal places.
	www.staff.vu.edu.au /mcaonline/units/numbers/numrou.html (614 words)

	Rounding Numbers: EnchantedLearning.com
		When a decimal number is rounded to the tenths place, the final form has no digit in the hundredths place (or any places to the right of that).
		To round off a number, the digit to be rounded either remains the same or is increased by one, and one or more of the digits on the right are eliminated or changed to zero.
		For example, 5 rounded to the tens digit is 0, 15 rounded to the tens digit is 20, and 185 rounded to the tens digit is 180.
	www.enchantedlearning.com /math/rounding (968 words)

	Php - Php Mysql - Rounding Tutorials
		Rounding by default is to zero decimal places, but the precision can be specified with the optional precision argument.
		The 4/5 rounding rules determine if a number is rounded up or down based on the digits that are lost due to the rounding precision.
		For example, 10.4 rounds down to 10, and 10.5 rounds up to 11.
	www.brainbell.com /tutors/php/php_mysql/Rounding.html (109 words)

	Rounding to hundreds (Site not responding. Last check: 2007-11-07)
		Rounded numbers are easier to work with in your head.
		To round numbers to the nearest hundred, make the numbers that end in 1 through 49 into the next lower number that ends in 00.
		For example 424 rounded to the nearest hundred would be 400.
	members.aol.com /_ht_a/iongoal/g32round100.htm (117 words)

	Rules of Rounding
		Rounding to the nearest hundredth means rounding to two decimal places.
		Rounding to the nearest tenth means rounding to one decimal place.
		Rounding to the nearest whole number means rounding to the ones place.
	www.dtc.dla.mil /qa/RR.htm (314 words)

	Rounding to Nearest 10 or 100
		One example of the rounding process using concrete materials and a number line that can be clearly seen by all students.
		One example of the rounding process using drawings and a number line that can be clearly seen by all students.
		Learning how to use the talking digit in a number to round will really help you to round when you don’t have concrete materials and when you don’t have time to draw in order to round a number.
	coe.jmu.edu /mathvidsr/lessons/rnth/rnth_a.htm (1104 words)

	Math Forum - Ask Dr. Math Archives: Rounding Numbers
		If the digit to the right of your rounding digit is less than 5 (0 through 4), round down (drop all digits to the right of the digit you are rounding, replacing them with zeros).
		361 rounded to the nearest 10 is 360, which is a multiple of 10.
		361 rounded to the nearest 100 is 400, which is a multiple of 100.
	mathforum.org /library/drmath/sets/select/dm_rounding.html (375 words)

	Rounding Numbers
		When you have to round an answer, you are usually told how much to round it.
		It's simplest when you're told how many "places" to round to, but you should also know how to round to a named "place", such as "to the nearest thousandth" or "to the ten-thousandths place".
		Otherwise, it looks like you rounded to one decimal place, or to the tenths place, and your answer could be counted off as being incorrect.
	www.purplemath.com /modules/rounding.htm (416 words)

	Rounding - The GNU C Library
		All results are rounded to the smallest representable value which is greater than the result.
		All results are rounded to the largest representable value whose magnitude is less than that of the result.
		Rounding all such numbers to zero or 2^r would cause some algorithms to fail at 0.
	www.gnu.org /software/libc/manual/html_node/Rounding.html (422 words)

	Merlyn - Javascript Rounding 0 - J R Stockton (Site not responding. Last check: 2007-11-07)
		Rounding a Number to a String with a given number of decimal places, or in other formats, is often required.
		Rounding to two decimal places by arithmetic will, quite correctly, be controlled by the sign of the difference from 1.355.
		When rounding (or truncating) a number which may be either positive or negative, it is sometimes necessary to round either towards plus infinity or towards minus infinity.
	www.merlyn.demon.co.uk /js-round.htm (1972 words)

	Programmable Logic DesignLine \| An introduction to different rounding algorithms
		The most fundamental fact associated with rounding is that it involves transforming some quantity from a greater precision to a lesser precision; for example, rounding a reasonably precise value like $3.21 to the nearest dollar would result in $3.00, which is a less precise entity.
		As a point of interest, the symmetric versions of rounding algorithms are sometimes referred to as "Gaussian implementations." This is because the theoretical frequency distribution known as a Gaussian distribution – which is named for the German mathematician and astronomer Karl Friedrich Gauss (1777-1855) – is symmetrical about its mean value.
		Round-random: This may also be referred to as random rounding or stochastic rounding, where the term "stochastic" comes from the Greek stokhazesthai, meaning "to guess at." With this technique, in the case of "half-way" values, we effectively toss a metaphorical coin in the air and randomly (or pseudo-randomly) round the value up or down.
	www.pldesignline.com /howto/showArticle.jhtml;?articleID=175801189 (2514 words)

	Rounding Whole Numbers
		Rounding means changing a given number to the nearest ten, hundred, thousand, and so on.
		Rounding is a form of estimation that you use when an approximation is good enough.
		Rounding is also good to use so that you know what to expect for an answer.
	math10.edcentre.ca /bridgemath/numbers/roundwhole.php (327 words)

	Rounding Off Decimals
		Rounding off a decimal is a technique used to estimate or approximate values.
		Rounding is most commonly used to limit the amount of decimal places.
		After rounding, the digit in the place we are rounding will either stay the same, referred to as rounding down, or increase by 1, referred to as rounding up.
	cstl.syr.edu /fipse/Decunit/roundec/roundec.htm (620 words)

	www.formz.com \| products
		Rounding solutions are also offered for concave vertices and for non-planar sequences of edges called stitches.
		While controlled rounding allows you to apply rounding which is globally blended each time changes are made to the rounding parameters, plain rounding allows you to apply rounding in a multi-layered mode.
		The rounding operation in form·Z is able to handle some challenging cases and includes the ability to round a sequence of edges with different arc sizes.
	www.formz.com /products/formz/rounding.html (196 words)

	Crystal Reports: Rounding
		But there are other ways to do rounding and they may cause your report to display values that don’t match other systems or applications.
		So 12.5 will be rounded down to 12 (as in the example on the right) and a value of 13.5 will be rounded up to 14.
		The justification for bankers rounding is apparent when you imagine a list with a typical distribution of even and odd numbers.
	www.crystalkeen.com /articles/crystalreports/rounding.htm (606 words)

	significant figures and rounding
		As far as I can tell rounding of significant figures carries a certain degree of controversy and people will argue with you based on what they were taught at some point in their education.
		They explain that without bias half of the time the number is rounded up, to me this makes a lot of sense, after all as scientists we want to be as unbiased as humanly possible.
		If you are rounding a number to a certain degree of significant digits if the number following that degree is less than five the last significant figure is not rounded up, if it is greater than 5 it is rounded up.
	www.chem.tamu.edu /class/majors/commonfiles/sigfig.htm (1281 words)

	Embedded.com - Rounding Algorithms 101 Redux
		Thus, in the case of software implementations, or during analysis of a system using software simulation, this form of rounding is sometimes employed to determine the upper limit of the algorithm (that is, the upper limit of the results generated by the algorithm for a given data set) for use in diagnostic functions.
		Thus, in the case of software implementations, or during analysis of a system using software simulation, this form or rounding is sometimes employed to determine the lower limit of the algorithm (that is, the lower limit of the results generated by the algorithm for a given data set) for use in diagnostic functions.
		Also known as alternate rounding, this is similar in concept to the Round-Half-Even and Round-Half-Odd schemes discussed earlier, in that the purpose of this algorithm is to minimize the bias that can be caused by always rounding "half-way" values in the same direction.
	www.embedded.com /showArticle.jhtml?articleID=189601153 (5050 words)

	The Sea Shell Rounding Activity Page
		For example 84 rounded to the nearest ten would be 80.
		Numbers that end in a digit of 5 or more should be rounded up to the next ten.
		The number 58 rounded to the nearest ten would be 60.
	www.janbrett.com /piggybacks/rounding.htm (134 words)

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