2021년 2월 17일 (수) 08:29에 Pythagoras0님의 편집

2021-02-17T08:29:00Z

Pythagoras0: /* 메타데이터 */ 새 문단

2020-12-26T12:28:37Z

메타데이터: 새 문단

Pythagoras0: /* 노트 */ 새 문단

2020-12-21T03:38:03Z

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새 문서

== 노트 ==

# Significant figures are any non-zero digits or trapped zeros.<ref name="ref_4dce">[https://courses.lumenlearning.com/introchem/chapter/significant-figures/ Introduction to Chemistry]</ref>
# Significant figures of a number are digits which contribute to the precision of that number.<ref name="ref_4dce" />
# In addition, 120.00 has five significant figures since it has three trailing zeros.<ref name="ref_4dce" />
# The significance of trailing zeros in a number not containing a decimal point can be ambiguous.<ref name="ref_4dce" />
# The LEAST number of significant figures in any number of the problem determines the number of significant figures in the answer.<ref name="ref_b56d">[https://www.nku.edu/~intsci/sci110/worksheets/rules_for_significant_figures.html Rules for Significant Figures]</ref>
# The significant figures (also known as the significant digits or precision) of a number written in positional notation are digits that carry meaningful contributions to its measurement resolution.<ref name="ref_b7c6">[https://en.wikipedia.org/wiki/Significant_figures Significant figures]</ref>
# Significance arithmetic is a set of approximate rules for roughly maintaining significance throughout a computation.<ref name="ref_b7c6" />
# Zeros to the left of the significant figures (leading zeros) are not significant.<ref name="ref_b7c6" />
# Thus 1.20 and 0.0980 have three significant figures whereas 45,600 may have 3, 4 or 5 significant figures.<ref name="ref_b7c6" />
# Count how many significant figures are in a number, and find which digits are significant.<ref name="ref_ecc7">[https://www.calculatorsoup.com/calculators/math/significant-figures-counter.php Significant Figures Counter]</ref>
# Let's see if we can learn a thing or two about significant figures, sometimes called significant digits.<ref name="ref_4026">[https://www.khanacademy.org/math/arithmetic-home/arith-review-decimals/arithmetic-significant-figures-tutorial/v/significant-figures Intro to significant figures (video)]</ref>
# Before we go into the depths of it and how you use it with computation, let's just do a bunch of examples of identifying significant figures.<ref name="ref_4026" />
# But I think when you look over here, it makes a lot more sense why you only have three significant figures.<ref name="ref_4026" />
# The non-zero digits are going to be significant figures.<ref name="ref_4026" />
# The method of rounding to a significant figure is often used as it can be applied to any kind of number, regardless of how big or small it is.<ref name="ref_6717">[https://www.bbc.co.uk/bitesize/guides/zscq6yc/revision/3 Rounding to significant figures]</ref>
# When a newspaper reports a lottery winner has won £3 million, this has been rounded to one significant figure.<ref name="ref_6717" />
# Not all of the digits have meaning (significance) and, therefore, should not be written down.<ref name="ref_e39b">[http://chemistry.bd.psu.edu/jircitano/sigfigs.html Significant Figure Rules]</ref>
# Hence a number like 26.38 would have four significant figures and 7.94 would have three.<ref name="ref_e39b" />
# How will you know how many significant figures are in a number like 200?<ref name="ref_e39b" />
# In mathematical operations involving significant figures, the answer is reported in such a way that it reflects the reliability of the least precise operation.<ref name="ref_e39b" />
# Following the rules noted above, we can calculate sig figs by hand or by using the significant figures counter.<ref name="ref_f9d5">[https://www.omnicalculator.com/math/sig-fig Significant Figures Calculator - Sig Fig]</ref>
# Suppose we have the number 0.004562 and want 2 significant figures.<ref name="ref_f9d5" />
# Suppose we want 3,453,528 to 4 significant figures.<ref name="ref_f9d5" />
# many of the following numbers have 4 significant figures?<ref name="ref_5117">[http://www.uky.edu/~garose/signfig.htm SIGNIFICANT FIGURE RULES]</ref>
# Only those digits before the exponent are used to express the number of significant figures.<ref name="ref_5117" />
# Exact numbers are considered to have an infinite number of significant figures.<ref name="ref_5117" />
# By using significant figures, we can show how precise a number is.<ref name="ref_6fc2">[http://www.chemistry.wustl.edu/~coursedev/Online%20tutorials/SigFigs.htm Significant Figures and Units]</ref>
# With significant figures, the final value should be reported as 1.3 x 102 since 0.46 has only 2 significant figures.<ref name="ref_6fc2" />
# It should be noted that both constants and quantities of real world objects have an infinite number of significant figures.<ref name="ref_96db">[https://chem.libretexts.org/Bookshelves/Analytical_Chemistry/Supplemental_Modules_(Analytical_Chemistry)/Quantifying_Nature/Significant_Digits Significant Digits]</ref>
# For example if you were to count three oranges, a real world object, the value three would be considered to have an infinite number of significant figures in this context.<ref name="ref_96db" />
# When rounding numbers to a significant digit, keep the amount of significant digits wished to be kept, and replace the other numbers with insignificant zeroes.<ref name="ref_96db" />
# When doing calculations for quizzes/tests/midterms/finals, it would be best to not round in the middle of your calculations, and round to the significant digit only at the end of your calculations.<ref name="ref_96db" />
# One way is to look at significant figures.<ref name="ref_5f62">[https://www-users.york.ac.uk/~mb55/msc/maths/sigfig.htm Brush up your maths: Significant figures]</ref>
# We round a number to three significant figures in the same way that we would round to three decimal places.<ref name="ref_5f62" />
# If the last significant digit of a number is 0, we include this.<ref name="ref_5f62" />
# To do my rounding, I have to start with the first significant digit, which is the 7.<ref name="ref_d17e">[https://www.purplemath.com/modules/rounding2.htm Rounding and Significant Digits]</ref>
# We say that 168 has three significant figures (i.e. three digits in the number are known to be correct), but 168.000 has six significant figures.<ref name="ref_8c92">[http://web.mit.edu/10.001/Web/Course_Notes/Statistics_Notes/Significant_Figures.html Significant Figures]</ref>
# Non-zero digits always count toward the number of significant figures; zeroes count except where they are only setting the scale.<ref name="ref_8c92" />
# Almost always you do not know the True Value, and the uncertainties you report (by how many significant figures you write down) are only estimates.<ref name="ref_8c92" />
# , so I confidently say I weigh 168 lbs (three significant figures).<ref name="ref_8c92" />
# Scientists express the level of precision by using significant figures.<ref name="ref_2239">[https://www.texasgateway.org/resource/significant-figures Significant Figures]</ref>
# When working with analytical data it is important to be certain that you are using and reporting the correct number of significant figures.<ref name="ref_7d68">[https://www.inorganicventures.com/icp-guide/significant-figures-and-uncertainty Significant Figures and Uncertainty]</ref>
# The number of significant figures is dependent upon the uncertainty of the measurement or process of establishing a given reported value.<ref name="ref_7d68" />
# In a given number, the figures reported, i.e. significant figures, are those digits that are certain and the first uncertain digit.<ref name="ref_7d68" />
# However, we know how difficult it is to make trace measurements to 3 significant figures and may be more than a little suspicious.<ref name="ref_7d68" />
# If your instructor has enabled it, the sigfig icon is displayed beside the answer box for questions that check for significant figures.<ref name="ref_cc17">[https://www.webassign.net/manual/student_guide/t_s_answering_numerical_sigfigs.htm Answering Numerical Questions That Check Significant Figures]</ref>
# The answer format tip indicates that a number must specified to the correct number of significant figures, and might also specify whether units are required.<ref name="ref_cc17" />
# In many of the problems in these tutorials, you will be asked to report your answer with a specific number of significant figures.<ref name="ref_1584">[http://chemcollective.org/activities/tutorials/stoich/significant_figures Significant Figures]</ref>
# When multiplying or dividing, the number of significant figures in the result is equal to the smallest number of significant figures in one of the operands.<ref name="ref_1584" />
# The operand with the smallest number of significant figures is 4.3, so our answer should have 2 significant figures.<ref name="ref_1584" />
# The same principle governs the use of significant figures in multiplication and division: the final result can be no more accurate than the least accurate measurement.<ref name="ref_41f8">[http://chemed.chem.purdue.edu/genchem/topicreview/bp/ch1/sigfigs.html Significant Figures]</ref>
# Determine the correct number of significant figures.<ref name="ref_41f8" />
# In some cases the originator of the information can provide an excess of true figures and the number is rounded off to contain only the necessary significant figures.<ref name="ref_025d">[https://acutecaretesting.org/en/articles/significant-figures Significant figures]</ref>
# If there is no indication of the uncertainty, the reader has (no other possibility than) to expect the number to contain only significant figures, the last of which is uncertain.<ref name="ref_025d" />
# Round the uncertainty to two significant figures.<ref name="ref_025d" />
# Start with rounding the uncertainty to two significant figures, i.e. 33 mg.<ref name="ref_025d" />
# Error Analysis and Significant Figures Errors using inadequate data are much less than those using no data at all.<ref name="ref_aed6">[https://www.ruf.rice.edu/~bioslabs/tools/data_analysis/errors_sigfigs.html Error Analysis and Significant Figures]</ref>
# You should only report as many significant figures as are consistent with the estimated error.<ref name="ref_aed6" />
# The quantity 0.428 m is said to have three significant figures, that is, three digits that make sense in terms of the measurement.<ref name="ref_aed6" />
# The same measurement in centimeters would be 42.8 cm and still be a three significant figure number.<ref name="ref_aed6" />
# Significant figures give an idea of the accuracy of a number.<ref name="ref_c62e">[http://mathsfirst.massey.ac.nz/Algebra/Decimals/SigFig.htm Significant Figures, Maths First, Institute of Fundamental Sciences, Massey University]</ref>
# We can use significant figures to show the difference.<ref name="ref_c62e" />
# Unless you actually see a red hint telling you that the significant figures are incorrect, then the reason for your answer being marked wrong has nothing to do with sig figs.<ref name="ref_f368">[https://depts.washington.edu/phys1xxz/webassign.php?page_type=sigfigs Physics 1XX Labs: WebAssign & Significant Figures]</ref>
# That number determines how many significant figures there must be in order for the question to be marked correct.<ref name="ref_f368" />
# The uncertainty can affect the required number of significant figures in the value.<ref name="ref_f368" />
# The uncertainty should be stated with 1 or 2 significant figures.<ref name="ref_f368" />
# How would you round a number like 99.99 to three significant figures?<ref name="ref_2885">[https://sites.google.com/site/chempendix/significant-figures Significant Figures]</ref>
# The number of significant figures in the product or quotient of two or more measurements cannot be greater than that of the measurement with the fewest significant figures.<ref name="ref_2885" />
# Here, the mantissa of the number to be logged is underlined, showing 3 significant figures.<ref name="ref_da06">[https://www.chm.uri.edu/weuler/chm112/lectures/logsigfigs.html CHM 112 Sig Figs for logs]</ref>
# The same number of significant figures is underlined starting with the decimal point.<ref name="ref_da06" />
# Significant figures are a central concept to reporting values in science, but one that is commonly misunderstood.<ref name="ref_4e15">[https://www.matrix.edu.au/everything-you-need-to-know-about-significant-figures-for-chemistry/ Everything You Need To Know About Significant Figures For Chemistry]</ref>
# Reading the value from left to right, the first non-zero digit is the first significant figure.<ref name="ref_4e15" />
# If the value does not have a decimal point, all digits to the right of the first significant figure to the last non-zero digit are significant.<ref name="ref_4e15" />
# For example, \( 100 \) could be a value given to \( 1, 2 \mbox{or} 3 \) significant figures.<ref name="ref_4e15" />
# so we know how many significant figures to round to at the end of the entire calculation.<ref name="ref_2611">[https://www.varsitytutors.com/ap_chemistry-help/significant-figures Significant Figures]</ref>
# Our answer from the addition should then only have 4 significant figures.<ref name="ref_2611" />
# Since the rules for significant figures for addition and subtraction are the same, our answer here should only have 2 significant figures.<ref name="ref_2611" />
# Round the final answer to 2 significant figures to reflect the least amount of significant figures found in the division.<ref name="ref_2611" />
# What has been done is round each of 10.65, 185, 0.3048 to one significant figure.<ref name="ref_f516">[https://www.open.edu/openlearn/science-maths-technology/mathematics-statistics/rounding-and-estimation/content-section-1.5 Rounding and estimation]</ref>
# Thus 10.65 is rounded to 10 (the 1 is the significant figure); 185 has been rounded to 200 (the 2 is the significant figure); and 0.3048 has been rounded to 0.3 (the 3 is the significant figure).<ref name="ref_f516" />
# To round to a given number of significant figures, first count from the first significant digit to the number required (including zeros).<ref name="ref_f516" />
# When a number is rounded, the number of significant figures is known as the precision of the number.<ref name="ref_f516" />
# Significant figures are numbers that carry a contribution to a measurement and are useful as a rough method to round a final calculation.<ref name="ref_4587">[https://www.steris-ast.com/techtip/significant-figures/ What Are Significant Figures?]</ref>
# Significant figures estimates should be made at the final step of the calculation.<ref name="ref_4587" />
# Significant figures are an important scientific concept in which it is assumed that all significant figures in a number are accurate except for the final digit.<ref name="ref_4068">[https://link.springer.com/article/10.1007/s11669-018-0662-z Significant Figures and False Precision]</ref>
# When the museum guide gave the age of the bones as 160,000,005 years old, the age became a number with nine significant figures.<ref name="ref_4068" />
# I am concerned when seeing manuscripts written with standard deviations having two or more significant figures.<ref name="ref_4068" />
# As shown in the following example, uncertainties with two or more significant figures add additional digits to the average.<ref name="ref_4068" />
# Once again using to many significant figures in the answer would be misleading.<ref name="ref_d823">[https://www.westfield.ma.edu/PersonalPages/cmasi/gen_chem1/sigfigs%20page/measurement_and_sigfigs.htm Measurement and SigFigs]</ref>
# So, how many significant figures should be used in your answer?<ref name="ref_d823" />
# The difference is 2.5 and this number is the number that limits the number of significant figures the answer can contain.....<ref name="ref_d823" />
# Exact numbers never limit the number of significant figures.<ref name="ref_d823" />
# So when you report 4500 people attended the game, you really have three significant figures.<ref name="ref_80fe">[https://www.rpi.edu/dept/phys/Dept2/APPhys1/sigfigs/sigfig/node12.html When is a zero significant?]</ref>
# The number of significant figures of a multiplication or division of two or more quantities is equal to the smallest number of significant figures for the quantities involved.<ref name="ref_16aa">[https://mathworld.wolfram.com/SignificantDigits.html Significant Digits -- from Wolfram MathWorld]</ref>
# For addition or subtraction, the number of significant figures is determined with the smallest significant figure of all the quantities involved.<ref name="ref_16aa" />
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 * ID :  [https://www.wikidata.org/wiki/Q1056761 Q1056761]

← 이전 판		2020년 12월 26일 (토) 12:28 판
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		+	* ID : [https://www.wikidata.org/wiki/Q1056761 Q1056761]

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2021년 2월 17일 (수) 08:29에 Pythagoras0님의 편집

Pythagoras0: /* 메타데이터 */ 새 문단

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