CHAPTER 2 VIDEO NOTES
CHEMISTRY 1
SIGNIFICANT FIGURES IN MEASUREMENTS
DR. CASAGRANDE
III. ACCURACY & PRECISION IN MEASUREMENTS
Follow along and complete these notes as you view video “#3: Accuracy & Precision in Measurements” at
https://youtu.be/f9WZuegmSto.
Measurements
•
Accuracy – how close a measurement is to
o
•
Closer is
the actual (accepted) value
more accurate
Precision – how close a set of measurements are to
o
Smaller spread is
each other
more precise
Examples using targets:
(Note: it is “accepted” that the bull’s eye is the place everyone aims for.)
• Accurate and precise
o Small spread in data can be reduced by using
o
•
•
•
more precise
equipment or improving technique
§ Random error—measurement inconsistencies
remove its effects by averaging data
§ Should always use smallest device that get the job done
, with
the most calibration markings
o e.g. use 10-mL graduated cylinder, not 50-mL graduated cylinder or 600 mL-beaker
for measuring 10.00 mL of liquid
Precise but not Accurate
o Consistency in technique
o Systematic error: due to bad design or mis-reading equipment: affects
accuracy
§ Example: mis-aligned scope on a rifle; uncalibrated balances.
§ Eliminate by fixing equipment (calibrating), improving procedure
Accurate but not precise
o Taking average gives accepted answer
o Spread in data too large
• Improve technique (practice) or
procedure
Neither precise nor accurate
o The average is off and the spread is large
o Need to improve technique
o Need to check equipment & procedure
Measuring Accuracy
• Want error to be 0
o Measure difference between experimental
result:
Percent Error =
data and accepted result as a percentage of accepted
( Experimental − Accepted ) × 100%
Accepted
where Error = ( Experimental − Accepted )
§ We take absolute value of the error because its sign is unimportant.
o Example: The accepted density for Cu is 8.92 g/cm3. What is the % error if a student obtains a value of 8.42
g/cm3 for the density of Cu?
(8.42 g/cm − 8.92 g/cm ) × 100% = 5.6%
% Error =
3
3
8.92 g/cm 3
Practice
•
The accepted density of gold (Au) is 19.3 g/cm3. A student measures the following densities for 3
samples of Au: A: 19.0 g/cm3, B: 19.7 g/cm3 and C: 19.1 g/cm3. Which measurement is most accurate?
(19.0 g/cm − 19.3 g/cm ) × 100% = 1.6%
A: % Error =
3
3
19.3 g/cm 3
(19.7 g/cm − 19.3 g/cm ) × 100% = 2.1%
B: % Error =
3
3
19.3 g/cm 3
(19.1 g/cm − 19.3 g/cm ) × 100% = 1.0%
C: % Error =
3
3
19.3 g/cm 3
•
C is the most accurate measurement since its
% error is smallest.
IV. SIGNIFICANT FIGURES IN MEASUREMENTS
Follow along and complete these notes as you view video “#4: Significant Figures in Measurements” at
https://youtu.be/LGD_AAVMLCw.
Precision in Measurements
• Measurements (3.25 cm) are different from other numbers (3.14159265, 25 students).
Measurements represent an action by someone with some measuring instrument.
Measurements have built-in uncertainty
No measurement is exact.
This uncertainty is the result of random differences in reading the measuring device
The amount of the uncertainty (precision) depends on how fine the markings (calibrations) are on the
measuring device
Measurements have units.
o
o
o
o
o
•
2
Significant Figures in Measurements Video Notes
•
The uncertainty in a measurement needs to be communicated.
o
o
o
Significant figures explicitly show the
precision to which a measurement is able to be made
Read to the smallest division (these are the certain digits), then estimate one more digit
(the estimate)
For electronic equipment, such as our balances, the last digit is electronically estimated, which is why it
often fluctuates (varies)
STUDENT NOTES Pre-AP Chemistry
U N I T 2 | Page 5
o In the following measurement, the ruler is marked to 10 cm divisions. It is read to the closest 1 cm, which
Example 2-3. Convert to scientific notation.
is estimated.
VALUE
SCIENTIFIC NOTATION
VALUE
SCIENTIFIC NOTATION
75100000
0.00000231
─234900
0.95000
9260
The
most precisely you can read the length of the pencil─0.00003549
is 9 cm, or 1
significant figure.
This ruler is marked to 1 cm divisions. By adding calibrations at 1 cm intervals, you add a level of precision
the ruler
and can
read the form.
length of the pencil to one more decimal place, or 0.1 cm:
Exampleto2-4.
Convert
to decimal
o
VALUE
5.39 x 107
DECIMAL NOTATION
1.12 x 103
VALUE
5.39 x 10─7
DECIMAL NOTATION
1.12 x 10─3
Now the5scientist is certain about the 9 and can estimate one more place,
so she can report the length as 9.4
─5
─2.35 x
1
0
─2.35 x
1
0
cm. Notice that some people might disagree and read it as 9.3 cm or 9.5. This is the random error in the
measurement. The 9 is certain and the 0.3, 0.4, or 0.5 is estimated, giving us 2 significant figures.
Example
2-5.ruler
Perform
the to
following
mathematical
functions
express the
answer
in correct
scientificinnotation.
o This
is marked
0.1 cm divisions.
It is estimated
toand
the closest
0.01
cm. This
is the precision
the
measurement
of
length
that
we
will
use
in
class:
EQUATION
ANSWER
EQUATION
ANSWER
3.20 x 103 + 9.77 x 102 =
3.20 x 103 x 9.77 x 102 =
3.20 x 103 - 9.77 x 102 =
3.20 x 103
9.77 x 102 =
Now you can be
certain of the 9.4 and we must estimate to the 0.01 cm. Thus you may say 9.42 cm, 9.43 cm,
IV. SIGNIFICANT
FIGURES:
or 9.44 cm. Thus the 9 and 0.4 are certain, and the 0.02, 0.03, or 0.04 are estimated, giving us 3 significant
What
is significant
in a calculation? Last unit we learned how to determine the number of significant
figures
.
easuring. We need , tthe
o take this aof
step urther…..
• As figures the size w
ofhen the m
divisions
decreases
precision
thefmeasurement
and the number of sig figs increases
WARNING!! IfIfyou
you do
do not
not use
of of
significant
figures
in your
on
WARNING!!
use the
thecorrect
correctnumber
number
significant
figures
in answer
your answer
labs,
quizzes
tests,you
youwill
willbebeZAPPED
ZAPPEDwith
withaasmall,
small,but
but significant
significant deduction!
So,So,
be be
on
quizzes
&&
tests,
deduction!
sure
you
use
the
rules...they
really
are
significant!
sure you use the rules…they really are significant!
A. Guidelines for Determining the number of Significant Figures/Digits…
Practice:
• Determine
the distances
by is
thesignificant.
following arrows, to the correct significant figures:
1. Any
digit thatindicated
is not zero
2. Zeros between nonzero digits are significant.
3. Zeros to the left of the first nonzero digit are not significant. These zeros are used to indicate the
placement of the decimal point.
4. If the number is greater than one, all zeros written to the right of the decimal point count as
significant.
5. Numbers that do not contain decimal points, the trailing zeros (i.e. zeros after the last nonzero digit)
0.50 cm
3.28 cm
5.50 cm 7.00 cm 8.29 cm
may or may not be significant. We will assume they are not significant.
Significant Figures in Measurements Video Notes
3
Now, do we want to memorize all of these rules??!?!? NOOOOOOOOOOOOOOO of course not! So, there’s a Determining The Number Of Significant Figures
•
All non-zero
digits and any zeroes between them ARE significant (assume these #s represent
measurements)
➂
➄
504
|||
•
83401
|||||
➃
6001
||||
If a decimal point is present, the largest
magnitude (place) non-zero digit is the most significant
figure. Digits to the right are significant (precision of measurement)
o Any zeroes to the left are magnitude zeroes, used to maintain the correct size of the number
o
Important to value but not significant (not precision)
➁
➂
0.0023
||
o
0.0000901
|||
Any zeroes after the last non-zero digit ARE
§
➀
➂
0.00000003
|
0.0517
|||
significant
Adding another zero would not change the size of the number, so it would be for precision
➁
➄
25.0
|| |
•
➅
200.002
||| |||
340.20
||| | |
➃
0.0006200
| |||
➂
100.
|||
With no decimal point, zeroes after the last non-zero digit are only magnitude zeroes
o Adding another zero would change the size of the number
➀
➁
➂
➄
70
|
12,000
||
801,000
|||
240,090
||| ||
o For numbers in scientific notation, all digits in the coefficient (not the exponent) are significant
(there is a dec. pt.)
➁
➃
➄
➂
3
–12
24
125
3.0×10
||
8.090×10
| |||
4.0000×10
| ||||
1.70×10
| ||
o Counted numbers and defined numbers (e.g. conversion factors or standard values) are exact
numbers with unlimited (infinite) significant figures
§ 12 eggs, 100 pencils, $1,200
§ 12 in/ft, 1000 mg/g, 16 oz/lb
You Practice
Determine the number of sig figs in each of the following numbers.
VALUE
VALUE
SF
250 cm
2
0.00009 s
1
3.99 kg
3
9.8801 L
5
100 forks
∞
(count)
2
0.0045 g
4
SF
2
4000 km
1
100 cg/g
∞
(defined)
4.0×10–3 g
4.00×10–3 cm3
3
Significant Figures in Measurements Video Notes