1. (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
650,462,932,028,450,284,737.2 23

2. 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
____________  ______________ _________________ g g
12.36  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)

3. 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
____________  ______________ _________________ g 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
____________  ______________ _________________

4. 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

5. 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 ______ )

6. (Case #2 continued) Counting significant figures
Rule 1: any nonzero digit is a significant figure (that’s easy)
Rule 2: zeros… oh so troublesome…. g
miles
sec
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
g miles
these zeroes are telling us ______________________
called _________________
in what place the number starts
place holders

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

8. (Case #2 continued) Counting significant figures
Rule 2b.. zeroes in between nonzero digits ___________________
ARE significant figures
302.1 mL g 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 g
___ SF (minimum uncertainty __________ ) 6
 1 g
certain
estimated

10. 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 g
___ SF (minimum uncertainty
______________ ) 7
 g
placeholders…
NOT SF
yes, SF
because
____________
yes, SF
because ___________________
decimal point IS present
b/w nonzero digits

11. 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
sec
___ SF (minimum uncertainty _______ ) 7
 1 sec
yes, SF
because ___________________
yes, SF
because
____________
decimal point IS present
b/w nonzero digits

12. (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
sec
___ SF (minimum uncertainty _______ ) 7
 1 sec
yes SF
because ___________________
yes, SF
decimal point IS present
estimated
sec
___ SF (minimum uncertainty _______ ) 5
 100 sec
not SF
because ___________________
yes, SF
decimal point is NOT present

13. (Case #2 continued) Counting significant figures
Rule 2c.. zeroes to the right of ALL nonzero digits ___________________
depends…..
estimated
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
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

14. (Case #2 continued) Counting significant figures
Rule 2c.. zeroes to the right of ALL nonzero digits ___________________
depends…..
estimated
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…
sec
( 10) sec
 106 sec

16. 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.

17. Precision / Significant Figures for calculated values
g 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
(  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

18. 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

19. Precision / Significant Figures for calculated values
Multiplication and Division
163.9 cm  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
(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

20. determine the #SF for each value in the calculation
Precision / Significant Figures for calculated values
Multiplication and Division
163.9 cm  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)

21. Precision / Significant Figures for calculated values
Addition and Subtraction
g 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
the first estimated digit
(min. unc. _____ )
 100
5 SF
the minimum uncertainty on the answer will be
______________________________
equal to the largest of the uncertainties
on the values in the calculation

22. determine the uncertainty for each value in the calculation
Precision / Significant Figures for calculated values
Addition and Subtraction
g g = ____________________
___ SF ____ SF
(min. unc. _____) (min. unc. _______ ) 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)

23.  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