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Topic: Significant digits


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In the News (Thu 31 Dec 09)

  
  Significant Digits
The last digit given for a measurement is always assumed to be estimated and it is significant.
All nonzero digits in a measurement are significant (1,2,3,4,5,6,7,8,9).
The number of significant digits in a measurement is an indication of the precision with which the measurement was taken.
www.hazelwood.k12.mo.us /~grichert/sciweb/phys8.htm   (798 words)

  
  Significant figures - Wikipedia, the free encyclopedia
The hypothetical idea of significant figures (sig figs or sf), also called significant digits (sig digs) is a method of expressing error in measurement.
Sometimes the term is used to describe some rules-of-thumb, known as significance arithmetic, which attempt to indicate the propagation of errors in a scientific experiment or in statistics when perfect accuracy is not attainable or not required.
The basis of significant figures is that of rounding, and rounding in itself reduces the accuracy of the measurement (this is because rounding is a technique that fundementally uses addition or subtraction - thus creating artificial error by the amount added or subtracted during rounding).
en.wikipedia.org /wiki/Significant_digit   (1020 words)

  
 Significant figures -- Facts, Info, and Encyclopedia article   (Site not responding. Last check: 2007-11-05)
Significant figures (also called significant digits and abbreviated sig figs or sig digs, respectively) is a method of expressing errors in (The act or process of measuring) measurements.
Leading zeros are therefore not considered significant, except that conventionally a number with value zero is considered to have one significant digit.
For example, appears to have four significant digits; the bar indicates that in fact the second zero is the last significant digit.
www.absoluteastronomy.com /encyclopedia/s/si/significant_figures.htm   (705 words)

  
 Significant figure : Significant digit   (Site not responding. Last check: 2007-11-05)
Rounded to two significant figures, we have 4,200; to three significant figures, it is 4,220; to 5 significant figures we have 4,215.0 and to 7 significant digits we get 4,215.025.
When adding, it isn't the number but the position of the significant figures that determines the significant figures of the result: if the first summand has significant digits which are to the right of the significant digits of the second summand, then these digits are insignificant in the result.
For example, adding 2103.45 (6 significant digits) to 3.453245 (7 significant digits) on a calculator results in 2106.903245, but this should be stated with 6 significant digits as 2106.90.
www.termsdefined.net /si/significant-digit.html   (740 words)

  
 The Number of Significant Digits   (Site not responding. Last check: 2007-11-05)
Significant digits are all the numbers that are certain, and one digit that contains some uncertainty.
significant digits in 30,000, because it is uncertain at the thousands place.
Every digit in a number in scientific notation is a significant digit.
www.carlton.paschools.pa.sk.ca /chemical/Sigfigs/number_of_significant_digits.htm   (483 words)

  
 ipedia.com: Significant figures Article   (Site not responding. Last check: 2007-11-05)
Significant Figures is a method used to determine propagation of error in a scientific experiment or in statistics when complete precision is not attainable or not required.
Significant Figures (also called sig figs, significant digits, or sig digs) is a method used to determine propagation of error in a scientific experiment or in statistics when complete precision is not attainable or not required.
The significant figures method teaches that when measuring using a non-electronic instrument, the observer should estimate within the nearest tenth of a division marked on the instrument.
www.ipedia.com /significant_figures.html   (678 words)

  
 SIGNIFICANT DIGITS
Rule 2:  The right-most non-zero digit is called the least significant digit except when there is a decimal point in the number, in which case the right-most digit, even if it is zero, is called the least significant digit.
Significant digits are determined by counting the number of digits from the most significant digit to the least significant digit.
When adding or subtracting numbers which represent measurements, the right­most significant digit in the sum is in the same position as the left-most significant digit in the numbers added or subtracted.
www.tpub.com /doemathematics/mathematics23.htm   (684 words)

  
 SBU Chemistry Significant Figures
The number of significant figures in a computed quantity may be the same or different from those of the quantities from which it is computed.
In general, the number of significant figures in a multiplication or division of quantities will be that of the quantity with the least number of significant figures.
The only times that 0 is significant is when one or more of them occur between non-zero digits, or when one or more of them in a row is at the end of a string of non-zero digits.
www.ic.sunysb.edu /Class/che133/lectures/sigfigs.html   (1613 words)

  
 Lesson 2-3 Significant Digits
Significant digits, which are also called significant figures, are very important in Chemistry.
Placeholders, or digits that have not been measured or estimated, are not considered significant.
Below are some examples, which show the number of significant digits in a group of numbers, and an explanation why the digits are significant.
www.fordhamprep.com /gcurran/calsig.htm   (1157 words)

  
 math webpage
The way the significant digits are used is understood universally by scientists,engineers and anyone else who works with measurements.
When adding or subtracting the right most digit in the result should be in the same position as that in the least precise measurement.
When multiplying or dividing the number of significant digits in the result is the same as that of the measure of the least significant digits.
www.hhm.k12.nf.ca /mathdept/mathwebpage.html   (129 words)

  
 Significant Digits   (Site not responding. Last check: 2007-11-05)
Note that 0's can be significant: 1.000 N is expressed to 4 significant digits, but 1.0 N is expressed to only 2 digits.
Therefore, the work can be known only to 3 significant digits, and the correct result is obtained by rounding the answer to 7.00 J. Remember that the 0's are significant, because they show how many digits are known.
For example, 3.56E+4 has three significant digits, but 35600 could be interpreted as having five, since the zeros could be significant.
homework.phys.utk.edu /CAPA/digits.html   (307 words)

  
 Significant Figures   (Site not responding. Last check: 2007-11-05)
the number of significant figures in the result should be equal to the number of significant digits in the least precise number (the number with the fewest significant digits given).
When we express a number with three significant figures, what we are saying is that the first two digits are essentially exactly correct, and the last one is uncertain by a small amount (generally it is only uncertain by about ± 1).
the number of significant digits you use is simply the same number of significant figures as is the number with the fewest significant figures.
homepage.mac.com /dtrapp/SignificantFigures.html   (2793 words)

  
 Measurements and Uncertainties versus Significant Digits or Significant Figures
The “significant figures” method attempts to use a single decimal numeral to express both the center and the halfwidth of a distribution: the nominal value of the numeral encodes the center, while the length of the string of digits roughly encodes the halfwidth.
What’s often worse, the “significant figures rules” make it impossible to keep guard digits, which are important for reasons discussed in section 2.1.
At the other extreme, highly uncertain data may be highly significant; the significance can sometimes be made manifest by signal averaging or other data-reduction techniques, as exemplified in section 2.1.
www.av8n.com /physics/uncertainty.htm   (11785 words)

  
 Significant Digits
If you know how significant the digits are in any measurement, then you may be able to reduce your workload and produce more accurate and usable numbers in your laboratory.
A result of an analysis cannot be reported using more significant digits than the number of significant digits in the least accurate measurement used in the procedure.
For example, 75 mL of a sample (using a 100 mL graduated cylinder with an accuracy to two significant digits) is diluted with water into a 500.0 mL volumetric flask (with an accuracy to four significant digits).
www.mwpca.org /lab/digits.htm   (444 words)

  
 Freshmen Physics: Significant Digits   (Site not responding. Last check: 2007-11-05)
The fact that the last digit is uncertain supports the principle that measurements cannot be made with exact certainty.
The significant digits in measurements reflect the precision of the measuring instrument and the skill of the person using it.
Since, none of the digits in the measurement of the line of the example on the opposite page are zero, all the digits are significant.
www.bergen.org /AAST/projects/PhysicsCourse/sigfigs.html   (759 words)

  
 Significant Figures
The number of significant figures in a measurement, such as 2.531, is equal to the number of digits that are known with some degree of confidence (2, 5, and 3) plus the last digit (1), which is an estimate or approximation.
In this case, however, we count the significant figures in each measurement, not the number of decimal places: When measurements are multiplied or divided, the answer can contain no more significant figures than the least accurate measurement.
There are four significant figures in both the mass of the penny (2.531) and the number of grams in a pound (453.6).
chemed.chem.purdue.edu /genchem/topicreview/bp/ch1/sigfigs.html   (547 words)

  
 Significant Digits
The number of digits that you write down for a measurement is called the number of significant digits (or significant figures) in the measurement.
Notice that all three digits to the right of the decimal point are estimates, since they were found by adding at least one estimated digit.
All three digits of the intermediate result "729" must be estimates, since they are produced by multiplying by an estimated digit.
www.batesville.k12.in.us /physics/APPhyNet/Measurement/Significant_Digits.html   (984 words)

  
 Rounding and Significant Digits
Another consideration in rounding is when you have to round to "an appropriate number of significant digits".
has four significant digits (the zero in the tenths place means that the measurement was made accurate to the tenths place, and that there just happen to be zero tenths; the
In other words, the "appropriate" number of significant digits is two, and you would report (in your physics lab report, for instance) that the volume of the block is
www.purplemath.com /modules/rounding2.htm   (492 words)

  
 SIGNIFICANT DIGITS
The number of significant digits in an answer to a calculation will depend on the number of significant digits in the given data, as discussed in the rules below.
The number of significant digits in 8200 is at least two, but could be three or four.
When quantities are being added or subtracted, the number of decimal places (not significant digits) in the answer should be the same as the least number of decimal places in any of the numbers being added or subtracted.
www.physics.uoguelph.ca /tutorials/sig_fig/SIG_dig.htm   (472 words)

  
 SIGNIFICANT DIGITS
digit, even if it is zero, is called the least significant digit.
In the number 3270, 3 is the most significant digit, and 7 is the least significant digit.
In the number 27.620, 2 is the most significant digit, and 0 is the least significant digit.
www.tpub.com /content/doe/h1014v1/css/h1014v1_74.htm   (192 words)

  
 significant figures   (Site not responding. Last check: 2007-11-05)
Significant figures: meaningful digits in a measured quantity.
All measurements have some degree of uncertainty; how great the uncertainty is depends on both the accuracy of the measuring device and the skill of its operator.
Significant Figures (also called sig figs, significant digits, or sig digs) is a method used to determine propagation of...
www.1-in-miniatures.com /2/significant-figures.html   (544 words)

  
 Significant Digits and Rounding -- TC3 MATH200 (Brown)   (Site not responding. Last check: 2007-11-05)
It has six significant digits, not four, because only zeroes at the start of a number are non-significant.
The 4 and 8 are definitely significant, but just by looking at the number we can't tell whether it's accurate to the nearest whole number (4800, four significant digits), to the nearest ten (480x, three significant digits), or to the nearest hundred (48xx, two significant digits).
Scientific notation removes the guesswork about how significant a large number is. 9.3E7 has two significant digits; it is accurate to the nearest million miles.
www.acad.sunytccc.edu /instruct/sbrown/stat/rounding.htm   (1886 words)

  
 Significant Figures Calculator   (Site not responding. Last check: 2007-11-05)
Scientific notation may be used for large results or if the number of significant digits would be ambiguous otherwise.
The least significant decimal is the place that holds the last significant digit.
If the next digit is five it rounds up half the time and down half the time based on whether the previous digit is even or odd.
ostermiller.org /calc/significant_figures.html   (325 words)

  
 Review of Significant Digits for PHY 207 / Dr. Miner   (Site not responding. Last check: 2007-11-05)
In this course, the assignment sheets state that all answers are to be given to three significant digits.
All the data on the sheets is presented to at least three significant digits, and the constants provided have three significant digits.
When rounding to three digits, if the fourth digit is 5 or larger increase the third digit by one, otherwise retain the first three digits without change.
www.udayton.edu /~physics/gkm/ssigfigs.htm   (211 words)

  
 Significant Digits   (Site not responding. Last check: 2007-11-05)
The first three zeros would not be considered significant since they have no non-zero digits anywhere to their left.(Rule 3) The last four zeros would all be considered significant since each of them has the non-zero digit 4 to their left.
The digits 1, 2, 4, and 2 are all considered significant (Rule 1) All zeros are considered significant since they have non-zero digits somewhere to their left (Rule 2).
If the digit to the right of the last reported digit is a 5 follwed by either no other digits or all zeros, round it and all digits to its right off and if the last reported digit is odd round up to the next even digit.
members.aol.com /profchm/sig_fig.html   (1950 words)

  
 Significant Digits   (Site not responding. Last check: 2007-11-05)
Zeroes that come between the last non-zero digit and the understood decimal place are not significant.
When the digit(s) to be dropped is/are greater than 5, the last place retained is increased by 1.
When the digit(s) to be dropped is/are 5 exactly (5, 50, 500, etc), the last retained column is rounded off to be even.
www.chem.vt.edu /RVGS/ACT/notes/Sig._Digs.html   (181 words)

  
 Lesson 2-3 Significant Digits
Significant digits, which are also called significant figures, are very important in Chemistry.
Below are some examples, which show the number of significant digits in a group of numbers, and an explanation why the digits are significant.
Once the arrow hits a nonzero digit, it and all of the digits after it are significant.
www.fordhamprep.org /gcurran/sho/sho/lessons/lesson23.htm   (1169 words)

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