(back to) CHAPTER 1 Significant Figures (range) Precision – is about the _________________ on values tells us _______________________ ______________________________ significant figures definition: ________________________________________ ________________________________________________ leads to another description of precision the more significant figures…. _______________________________ uncertainty the first estimated digit in an answer and/or tells us how many digits are known for certain (w/ certainty) a significant figure is a digit within a number for which we have some certainty of its magnitude for us the ones we are certain of plus the first estimated digit the more precise the number 0.000000000000000004 650,462,932,028,450,284,737.2 23

well now…. just how does one figure out significant figures…. CASE #1: If you know the uncertainty (the ), figuring out SF is straightforward the answer is recorded to the first estimated digit reminder corresponds to the uncertainty ____________  ______________ _________________ 12.3672 g 0.02967 g 12.36  0.02 g 1. 2. the first digit estimated tell us we are firstly uncertain in the hundredths place by 2 certain 4 SF (the three we are certain of plus the first estimated)

well now…. just how does one figure out significant figures…. CASE #1: If you know the uncertainty (the ), figuring out SF is straightforward the answer is recorded to the first estimated digit reminder corresponds to the uncertainty ____________  ______________ _________________ 12.3672 g 0.02967 g 12.36  0.02 g 4 SF 1. 2. the first digit estimated tell us we are firstly uncertain in the hundredths place certain ____________  ______________ _________________

CASE #2: if you do NOT know the uncertainty, you must assume the author of the number has written the number with the correct number of significant figures includes: ___________________________ ___________________________________ most often the case the digits we are certain of plus the first estimated (the rightmost digit) ________ ______ 327 mL ____ SF (minimum uncertainty ______ ) 3  1 mL estimated certain

CASE #2: if you do NOT know the uncertainty, you must assume the author of the number has written the number with the correct number of significant figures includes: ___________________________ ___________________________________ most often the case the digits we are certain of plus the first estimated (the rightmost digit) ________ ______ 327 mL ____ SF (minimum uncertainty ______ ) 3  1 mL estimated certain ________ ______ ____ SF (minimum uncertainty ______ ) ________ ______ ____ SF (minimum uncertainty ______ )

(Case #2 continued) Counting significant figures Rule 1: any nonzero digit is a significant figure (that’s easy) Rule 2: zeros… oh so troublesome…. 0.00378090 g 4670004 miles 8093200. sec 8093200 sec zeroes: - to the left - in between nonzero digits - to the right Rule 2a.. zeroes to the left of ALL nonzero digits ___________________ are NOT significant figures 0.00378 g 009826 miles these zeroes are telling us ______________________ called _________________ in what place the number starts place holders

(Case #2 continued) Counting significant figures Rule 2a.. zeroes to the left of ALL nonzero digits ___________________ are NOT significant figures 0.00378 g 009826 miles these zeroes are telling us ______________________ called _________________ in what place the number starts place holders the first nonzero digit… the number starts here 0.00378 g ___ SF (minimum uncertainty __________ ) 3  0.00001 g certain estimated the first nonzero digit… the number starts here 009826 mi ___ SF (minimum uncertainty __________ ) 4  1 mi certain estimated

(Case #2 continued) Counting significant figures Rule 2b.. zeroes in between nonzero digits ___________________ ARE significant figures 302.1 mL 602091 g 4670004 in if these ARE SF, means that _____________________________________ we have knowledge of their magnitude and that magnitude is zero 302.1 mL ___ SF (minimum uncertainty __________ ) 4  0.1 mL certain estimated 602091 g ___ SF (minimum uncertainty __________ ) 6  1 g certain estimated

0.003780900 g (Case #2 continued) Counting significant figures Rule 2c.. zeroes to the right of ALL nonzero digits ___________________ - if a decimal point is present ________________________ - if a decimal point is not present _______________________ depends….. the zeroes ARE significant figures the zeroes are NOT significant figures the first nonzero digit… the number starts here estimated 0.003780900 g ___ SF (minimum uncertainty ______________ ) 7  0.000000001 g placeholders… NOT SF yes, SF because ____________ yes, SF because ___________________ decimal point IS present b/w nonzero digits

8093200. sec (Case #2 continued) Counting significant figures Rule 2c.. zeroes to the right of ALL nonzero digits ___________________ - if a decimal point is present ________________________ - if a decimal point is not present _______________________ depends….. the zeroes ARE significant figures the zeroes are NOT significant figures the first nonzero digit… the number starts here estimated 8093200. sec ___ SF (minimum uncertainty _______ ) 7  1 sec yes, SF because ___________________ yes, SF because ____________ decimal point IS present b/w nonzero digits

(Case #2 continued) Counting significant figures Rule 2c.. zeroes to the right of ALL nonzero digits ___________________ - if a decimal point is present ________________________ - if a decimal point is not present _______________________ depends….. the zeroes ARE significant figures the zeroes are NOT significant figures estimated 8093200. sec ___ SF (minimum uncertainty _______ ) 7  1 sec yes SF because ___________________ yes, SF decimal point IS present estimated 8093200 sec ___ SF (minimum uncertainty _______ ) 5  100 sec not SF because ___________________ yes, SF decimal point is NOT present

(Case #2 continued) Counting significant figures Rule 2c.. zeroes to the right of ALL nonzero digits ___________________ depends….. estimated 8093200. sec ___ SF (minimum uncertainty _______ ) 7  1 sec yes SF because ___________________ decimal point IS present yes, SF instrument was calibrated to (increment) ____________ so, could estimate to the _______________ 1  101 1’s place estimated 8093200 sec ___ SF (minimum uncertainty _______ ) 5  100 sec not SF because ___________________ decimal point is NOT present yes, SF instrument was calibrated to (increment) ____________ so, could estimate to the _______________ 1  103 100’s place

(Case #2 continued) Counting significant figures Rule 2c.. zeroes to the right of ALL nonzero digits ___________________ depends….. estimated 8093200 sec ___ SF (minimum uncertainty _______ ) 6  10 sec not SF yes SF instrument was calibrated to ____________ so, could estimate to the _______________ 100’s place yes SF 10’s place to represent… can’t put in a decimal point, and can’t leave it off… 8093200 sec 8093200 ( 10) sec 8.09320  106 sec

I meant what I said and I said what I meant I meant what I said and I said what I meant. An elephant's faithful one hundred percent.

Precision / Significant Figures for calculated values 432.06 g + 7900 g since each value in the calculation has uncertainty, the result will _________________________ also be uncertain Case 1: If you know the uncertainty on each value (432.06  0.02 g) + (7900  400 g) then the uncertainty for the answer _______________________ ___________________________________________________ ________________________________________ can be calculated from the uncertainties for each of the operands (propagated error) square root of the sum of the squares of the relative uncertainty on each of the values in the calculation….. from the uncertainty, the # of significant figures can be determined

Precision / Significant Figures for calculated values Case 2: If you aren’t given the uncertainties on each value in the calculation, then the uncertainty for the answer _________________________________________ these rules assume _________________________ __________________________ there is a set of rules for multiplication () and division (÷) and for addition (+) and subtraction (-) multiplication and division first…. is estimated based on a set of rules these rules determine the number of SF in the answer the uncertainty in the estimated digit is at least 1

Precision / Significant Figures for calculated values Multiplication and Division 163.9 cm  0.23 cm = ____________________ ___ SF ____ SF (min. unc. _____) (min. unc. _______ ) estimated digit 4 2  0.1  0.01 underline uncertain digits reminder – significant figures are the ones we are ____________________ plus ______________________ certain of 163.9  0.23 the first estimated digit 37 (min. unc. _____ )  1 4.917 2 SF 32.78 same number of SF in the answer as ______________________________ 37.697 for the value in the calculation with the fewest SF

determine the #SF for each value in the calculation Precision / Significant Figures for calculated values Multiplication and Division 163.9 cm  0.23 cm = ____________________ ___ SF ____ SF (min. unc. _____) (min. unc. _______ ) 37 cm2 estimated digit 4 2  0.1  0.01 Rule for  and ÷ determine the #SF for each value in the calculation identify the number of SF which is the fewest SF report the final answer to that # of SF (the least precise value governs #SF in answer)

Precision / Significant Figures for calculated values Addition and Subtraction 436200 g + 9012431.76 g = ____________________ ___ SF ____ SF (min. unc. _____) (min. unc. _______ ) estimated digit 4 9  100  0.01 underline uncertain digits reminder – significant figures are the ones we are ____________________ plus ______________________ certain of 436200 + 9012431.76 the first estimated digit 9448600 (min. unc. _____ )  100 9448631.76 5 SF the minimum uncertainty on the answer will be ______________________________ equal to the largest of the uncertainties on the values in the calculation

determine the uncertainty for each value in the calculation Precision / Significant Figures for calculated values Addition and Subtraction 436200 g + 9012431.76 g = ____________________ ___ SF ____ SF (min. unc. _____) (min. unc. _______ ) 9448600 g estimated digit 4 9  100  0.01 Rule for + and - determine the uncertainty for each value in the calculation identify the largest of the uncertainties report the final answer to agree in place with that uncertainty (the value with the greatest uncertainty governs the #SF)

 Precision / Significant Figures for calculated values NOTE 1: exact #’s uncertainty _____________ #SF ___________ uncertainty will be __________ #SF will be ___________ NOTE 2: these rules for SF in calculations may over or under estimate the # SF in the calculated answer… BUT,… this is the best we can do to determine precision without knowing the uncertainties for the values in the calculation  0  count defined the lowest the greatest