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This 5 page Class Notes was uploaded by Peggie Leffler on Saturday October 3, 2015. The Class Notes belongs to CHM115 at California State Polytechnic University taught by Staff in Fall. Since its upload, it has received 18 views. For similar materials see /class/218235/chm115-california-state-polytechnic-university in Chemistry and Biochemistry at California State Polytechnic University.
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Date Created: 10/03/15
CALIFORNIA STATE POLYTECHNIC UNIVERSITY POMONA UNDERSTANDING SIGNIFICANT FIGURES Dr ANZ A number has a string of digits and punctuation it represents size or magnitude of something real or abstract 00127934100 The comma is used here to show a grouping of 3 places in the number relative to the decimal point period The decimal point shows where the unit value is located and all the other positions in the number have a particular meaning depending on the base of the number system in use The decimal system is in common use and has counting integers 9 8 7 6 5 4 3 2 1 0 The positions of the digits have meaning decimal very signi cant mark The thousands hundreds tens units tenths hundredths thousandths etc Left lt l gt Right If there is a decimal point i The right most digit is the least significant figure even if it is a zero The left most non zero digit is the most significant digit 3 All digits between the least significant digit and the most significant digit are the number of significant digits in the number inclusive N 0 8 6 5 0 4 2 0 0 0 Number of lt Significant Example left most Figures 2 9 non zero digit most significant figure written in scientific notation 865042000 X 10 3 Note the coefficient contains all of the significant figures right most digit least significant figure If there is no decimal oint 1 The right most non zero digit is the least significant digit 2 All subsequent zeros are only magnitude marks The left most non zero digit is the most significant digit 3 All digits between the least significant digit and the most significant digit are the number of significant digits in the number inclusive Number of 391 Significant gt Figures 0 8 6 5 0 4 2 0 0 Example I I lt these places are used to determine the magnitude right most non zero digit least significant digit 0 left most non zero digit is the most significant figure written in scientific notation 865042 X 10 8 Note the coefficient contains all of the significant figures Scienti c Notation The number N is contained in the proper number of significant figures but should be expressed as a coefficient times multiplier of 10 to a power N 10 lt coefflt10x10J where J is integer where coefficient is written to proper number of significant figures and J is an integer Consider a number 37526 103 102101 100 101 37526 I The decimal has to move to the left to make the coefficient of the proper magnitude and this is equivalent to simultaneous multiplication by the position multiplier of 103 Thus the number in scientific notation is 37526 X 103 Greek Alphabet x alpha 8 epsilon i iota V nu p rho q phi B 2 beta C zeta K kappa i 2 xi 6 sigma x chi Y gamma T eta A lambda o omicron 1 tau I 2 psi 5 delta 9 theta u mu TE 2 pi 1 upsilon 0 omega SI Pre xes 100 unity 10391 deci d 101 deca da 10392 centi C 102 hecto h 103 milli m 103 ki10 k 10 6 2 micro 4 106 2 mega M 10 9 nano n 109 giga G 10712 2 Pi00 P 1012 tera T 103915 femto f 1015 peta P 1018 atto a 1018 exa E Learn them in reciprocal pairs such as 106 10 6 1 because multiplication by one does not change the value Examples eg Convert 343 km to cm immediately recognize that km E 103 m and cm 2 10 2 In so by ratio 1g1051lt 2105c direct substitution for k leads to 343 X 105 cm Another way 1 343 103 m 343 X 103 102 X 102 m Collect the prefix with units using by design 10 2 c 343 X 103 X 102 cm 2 343 X 105 cm combining powers Yet another way 100031 100 cm 343 m7 343 1000100 cm 2 343 103102 cm writing 1000 103 etc combining 343 105 cm This last technique is treating the problem as a conversion whereas the basic unit does not change it is a case of number presentation Propagation of Signi cant Figures in Calculation The propagation of signi cant figures in calculations is determined by the number of significant figures of the entries under consideration and the mathematical operation between them The rules are developed according to which operations are employed Generally do multiplication and division first to get the precision of that entry entries Then do addition and subtraction MultiplicatiomDivision For these operations the entries are factors of differing numbers of significant figures the result must have no more significant figures than the factor possessing the least number of significant figures Example 3 sig figs factor with least numbers of significant figures 3145592123951 2 1744 1696 Thus answer has only 3 sig figs 2 174 Thus residue 41696 is less than 50000 factor with least sig figs 7543i62363 11140068 round to 4 sig figs 2 1114 integer value does not determine number of sig figs AdditionSuth action For these operations the entries must be considered by number of significant figures relative to a decimal point The rule being that there can be no more significant figures to the right of the decimal than the entry with the fewest number of significant figures where all entries have the same multiplier 2 eg a 11 79 round to tenths 4067 4 round to tenths 07 39 4086 8 subtract 47 924 round to tenths 36 12l NOTE The additional precision in the number must be used to round and not just cast away The order it is done does not matter however it seems more economical to round them before the operation 4 De nitions Intensive property is a characteristic of material that describes its attributes or qualities which are uniformly distributed throughout the whole collection under discussion These characteristics are not directly additions within the category eg temperature pressure density color thermal conductance resistivity etc Extensive property is a characteristic of material that describes the quantity of the whole collection under discussion These characteristics are additives within the category e g volume mass amount of substance area resistance etc Types of Errors Systematic Error Also known as a determinate error these types of errors can be discovered and corrected for For example you could have used a meter stick that was 02 units too low Random Error Also known as an indeterminate error these types of errors can not be corrected for These errors arise from our limitations to make scientific instruments and hence limit our ability to make a measurement These errors are always present In order to clarify a printed presentation the scientist frequently uses symbols from other alphabets to represent physical variables
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