Do Now
• How long is this room?
• What value would you give for the distance is
from the white board and the wall behind the
safety shower?
• What do you think the error is in your value?
slide 1
How Long is this Room?
Measurement
Value Error
Method
Rationale for Error
slide 2
How Long is this Room?
Measurement
Value Error
Method
Eyeball
Estimate
60'
± 10'
Rationale for Error
Viewing a distance is not
terribly accurate
slide 3
How Long is this Room?
Measurement
Value Error
Method
Eyeball
Estimate
Count
Floor Tiles
Rationale for Error
Viewing a distance is not
terribly accurate
60'
± 10'
52'
Each tile is between 11.5"
± 26" and 12.5". Operator error
possible.
slide 4
How Long is this Room?
Measurement
Value Error
Method
Eyeball
Estimate
Count
Floor Tiles
Measuring
Tape
Rationale for Error
Viewing a distance is not
terribly accurate
60'
± 10'
52'
Each tile is between 11.5"
± 26" and 12.5". Operator error
possible.
52' 7"
± 2"
Tape might not be straight
and level. Operator error
possible.
slide 5
Measurement & Data Uncertainty
SWBAT:
Write this
in your
notes
1) properly report data based on the
limitations of measuring device used
2) distinguish between accuracy & precision
3) calculate error & percent error
slide 6
Two Types of Numbers
Write this
in your
notes
Exact Numbers
Measured Numbers
 Numbers that can be
counted
 Numbers obtained by a
measurement
– a dozen eggs
– 5 students
– Abby is 5' 7"
– a desk weighs 26 lbs
 Numbers with a defined
value
– 5280 feet in one mile
– Absolute zero is 0 K
No uncertainty in
the value
Uncertainty in value,
which is defined by
the measuring instrument
slide 7
Exact or Measured Value?
5 pool balls
exact
Ball diameter is 2.0"
measured
1 inch = 2.54 cm
1 inch is exact
2.54 probably measured
slide 8
Data
• Science is built on data (measured values)
• Any scientific conclusion is only as strong as the
data upon which it is built
• Measured values, however, cannot not be known
to complete certainty
• When gathering, using and communicating data,
it is very important the uncertainty of the data is
considered as well
• In today's class, we are going to learn terms and
practices for reporting measured values and
representing the uncertainty of data
slide 9
Write this in your notes
Proper Reporting of Measured Data
1) Report all known digits
•
All digit you can actually read off of the
measurement device
2) Report one estimated digit
•
One digit beyond what you can actually read off
of the measurement device
slide 10
1) All known digits
2) One estimated digit
3 cm is a known digit
0.5 cm is a known digit
0.07 cm is an estimated digit
Length with this ruler
3.57 cm
slide 11
Check for Understanding 1
Given this ruler as the measuring device, what is the
proper way to report the length of this metal rod?
5.23 cm
slide 12
Check for Understanding 2
• The volume of fluid in
a graduated cylinder is
read from the bottom
of the meniscus
(dotted white line)
• What is the proper
volume to report?
slide 13
Check for Understanding 2
• The volume of fluid in
a graduated cylinder is
read from the bottom
of the meniscus
(dotted white line)
• What is the proper
volume to report?
8.67 mL
slide 14
Each Value Reported Reflected the
Limitations of the Measurement Method
Measurement
Value Error
Method
Eyeball
Estimate
Count
Floor Tiles
Measuring
Tape
Rationale for Error
Viewing a distance is not
terribly accurate
60'
± 10'
52'
Each tile is between 11.5"
± 26" and 12.5". Operator error
possible.
52' 7"
± 2"
Tape might not be straight
and level. Operator error
possible.
slide 15
Accuracy & Precision
Write this
in your
notes
• Accuracy - how close data is to the true value
• Precision - how close multiple data points are to
each other
slide 16
Write this
in your
notes
slide 17
Aspects of Accuracy & Precision
• The two concept are independent of each other. A
change in one means nothing for the other
 High accuracy does not mean high precision
 High precision does not mean high accuracy
• For a single data point, one can speak of accuracy,
but not precision. Precision can only be applied to
two or more data points
• Accuracy can only be discussed if the true value is
known (often it is not)
slide 18
Analysis of Lab Data
• Three students measured the density of sucrose
• The true value is 1.59 g/mL
• Who is most accurate? Who is most precise?
Most accurate
Closest to true value
Most precise
Closest to each other
slide 19
Check for Understanding
Four students did experiments where they each ran three
trials to determine the atomic mass of carbon-12 (defined
value = 12). Their data sets are as follows:
a) Which set of data is most accurate?
b) Which set of data is most precise?
slide 20
Check for Understanding
Four students did experiments where they each ran three
trials to determine the atomic mass of carbon-12 (defined
value = 12). Their data sets are as follows:
a) Which set of data is most accurate? Kanye
b) Which set of data is most precise?
slide 21
Check for Understanding
Four students did experiments where they each ran three
trials to determine the atomic mass of carbon-12 (defined
value = 12). Their data sets are as follows:
a) Which set of data is most accurate? Kanye
b) Which set of data is most precise? Taylor
slide 22
Error & Percent Error
• When the true value for data is known, it is possible
to characterize the accuracy with numbers
Write this
in your
notes
• Error
𝒆𝒓𝒓𝒐𝒓 = 𝒆𝒙𝒑𝒆𝒓𝒊𝒎𝒆𝒏𝒕𝒂𝒍 𝒗𝒂𝒍𝒖𝒆 − 𝒂𝒄𝒄𝒆𝒑𝒕𝒆𝒅 𝒗𝒂𝒍𝒖𝒆
• Percent error
|𝒆𝒓𝒓𝒐𝒓|
𝒑𝒆𝒓𝒄𝒆𝒏𝒕 𝒆𝒓𝒓𝒐𝒓 =
𝒙 𝟏𝟎𝟎
𝒂𝒄𝒄𝒆𝒑𝒕𝒆𝒅 𝒗𝒂𝒍𝒖𝒆
• Percent error is used to give the reader a sense of
how big the error is relative to the measurement
itself
slide 23
Error & Percent Error
actual value = 1.59 g/mL
Beyonce
density
(g/mL)
Trial 1
1.54
Trial 2
1.60
Trial 3
1.57
Average
1.57
error
(g/mL)
percent
error
slide 24
Error & Percent Error
actual value = 1.59 g/mL
Beyonce
density
(g/mL)
error
(g/mL)
Trial 1
1.54
-0.05
Trial 2
1.60
+0.01
Trial 3
1.57
-0.02
Average
1.57
-0.02
percent
error
Sample Calculation
𝒑𝒆𝒓𝒄𝒆𝒏𝒕 𝒆𝒓𝒓𝒐𝒓 =
=
|𝒆𝒓𝒓𝒐𝒓|
𝒙 𝟏𝟎𝟎
𝒂𝒄𝒄𝒆𝒑𝒕𝒆𝒅 𝒗𝒂𝒍𝒖𝒆
|−𝟎.𝟎𝟓|
𝟏.𝟓𝟗
= 𝟑. 𝟏𝟒%
𝒙 𝟏𝟎𝟎
slide 25
Error & Percent Error
actual value = 1.59 g/mL
Beyonce
density
(g/mL)
error
(g/mL)
percent
error
Trial 1
1.54
-0.05
3.14%
Trial 2
1.60
+0.01
0.63%
Trial 3
1.57
-0.02
1.26%
Average
1.57
-0.02
1.26%
Sample Calculation
𝒑𝒆𝒓𝒄𝒆𝒏𝒕 𝒆𝒓𝒓𝒐𝒓 =
=
|𝒆𝒓𝒓𝒐𝒓|
𝒙 𝟏𝟎𝟎
𝒂𝒄𝒄𝒆𝒑𝒕𝒆𝒅 𝒗𝒂𝒍𝒖𝒆
|−𝟎.𝟎𝟓|
𝟏.𝟓𝟗
= 𝟑. 𝟏𝟒%
𝒙 𝟏𝟎𝟎
slide 26
Check for Understanding
actual value = 1.59 g/mL
Iggy says her results are so fancy, but what
are her error & percent error?
Iggy
density
(g/mL)
Trial 1
1.70
Trial 2
1.69
Trial 3
1.71
Average
1.70
error
(g/mL)
percent
error
slide 27
Check for Understanding
actual value = 1.59 g/mL
Iggy says her results are so fancy, but what
are her error & percent error?
Iggy
density
(g/mL)
error
(g/mL)
Trial 1
1.70
+0.11
Trial 2
1.69
+0.10
Trial 3
1.71
+0.12
Average
1.70
+0.11
percent
error
slide 28
Check for Understanding
actual value = 1.59 g/mL
Iggy says her results are so fancy, but what
are her error & percent error?
Iggy
density
(g/mL)
error
(g/mL)
percent
error
Trial 1
1.70
+0.11
6.92%
Trial 2
1.69
+0.10
6.29%
Trial 3
1.71
+0.12
7.55%
Average
1.70
+0.11
6.92%
slide 29
Homework
slide 30
Review
• An accurate measurement is close to the accepted value.
• A set of precise measurements shows little variation.
• The measurement device determines the degree of precision
possible.
• Error is the difference between the measured value and the
accepted value. Percent error gives the percent deviation
from the accepted value.
error = experimental value – accepted value
• The number of significant figures reflects the precision of
reported data.
• Calculations should be rounded to the correct number of
significant figures.
slide 31
Backup Slides
slide 32
Put homework in
the class basket
Do Now
Put out your
name card
Mary sewed a shirt for her boyfriend's
birthday. She shows you a photo (right)
and asks you to rate it on a scale of 1-10.
You say it is a "5".
Mary says you are wrong. She says 4
people have rated the shirt a "10". The
four people are her mother, father,
grandmother and boyfriend. She feels
that since 4 out of 4 people rated the shirt
a "10", then the shirt must be a "10"!!!
What do you think of Mary's conclusion?
slide 33
Aspects of Accuracy & Precision
• The two concept are independent of each other. A
change in one means nothing for the other
− High accuracy does not mean high precision
− High precision does not mean high accuracy
Mary confused high
precision for high
accuracy.
slide 34
http://chemwiki.ucdavis.edu/Analytical_Chemistry/Quantifying_Nature/Units_of_Measure
electrical
charge
1
mass
distance
time
1
1
SI unit, other typical units
electric charge
coulomb
mass
kilogram, gram, metric ton, pound
meter, foot, mile
second, day, year
liter, cm3, quart, fluidounce
kg m–3, g cm–3
newton, dyne
pascal, atmosphere, torr
1
1
1
3
–3
1
–1
–2
–2
length
time
volume
density
force
pressure
1
2
–2
energy
joule, erg, calorie, electron-volt
1
1
2
2
1
1
1
–1
1
2
3
–2
–3
–2
–1
–2
–1
–1
1
power
electric potential
electric current
electric field intensity
electric resistance
electric resistivity
electric conductance
watt
volt
ampere
volt m–1
ohm
1
1
1
1
–2
2
2
quantity
siemens, mho
slide 35