UNIT 1
TOPIC 11: MEASUREMENT AND DATA PROCESSING
Assessment Statements
Objective
11.1 Uncertainties and Error in Measurements





Describe and give examples of random uncertainties and systematic errors.
Distinguish between precision and accuracy.
Describe how the effects of random uncertainties may be reduced.
State random uncertainty as an uncertainty range (±).
State the results of calculations to the appropriate number of significant figures.
2
2
2
1
1
11.2 Uncertainties in calculated results


State uncertainties as absolute and percentage uncertainties.
Determine the uncertainties in results.
1
3
Sketch graphs to represent dependences and interpret graph behaviour.
Construct graphs from experimental data.
Draw best-fit lines through data points on a graph.
Determine the values of physical quantities from graphs.
3
3
1
3
CDO IB Chemistry SL/HL Trimble




Unit 1 2014-2015
11.3 Graphical techniques
1
Uncertainty in Measurements
o
Different measuring devices have
Estimating Uncertainty
o
To estimate a measuring devices uncertainty
Indicate using + after the recorded measurement
o
Example:
Significant figures - Counting
o
Counting Significant Figures – Atlantic Pacific Method
•
•
Decimal point absent (Atlantic) – begin on right side of number
•
Decimal point present (Pacific) - begin on left side of number
Exact numbers –
CDO IB Chemistry SL/HL Trimble
o
Unit 1 2014-2015
Indicating uncertainty in a measurement
2
Examples: Counting Sig. Figs
234 cm
67000 cm
45000 cm
560. cm
0.5630 cm
1.0034 cm
0.00467 cm
Used to
o
Standard Form

Base –

Exponent –

Negative Exponent –

Positive Exponent –
Examples: Scientific Notation
124300 =
0.00362 =
1300000 =
1.23E-5 =
5.61 x 10^6 =
CDO IB Chemistry SL/HL Trimble
o
Unit 1 2014-2015
Scientific Notation
3
Calculators and Scientific Notation
o
Calculators handle scientific notation by only inputting the exponent,

o
enter the base as you would a regular number,
Display –
Experimental errors
Random errors - Precision
•
Random errors - Precision
•
A random error makes the measured value
•
Reduce random errors-
Systematic error -
•
Errors due to
•
Makes the measured value
•
An experiment may involve
Categories of systematic errors
•
Personal errors -
•
Instrumental Errors –
•
Method Errors -
CDO IB Chemistry SL/HL Trimble
•
Unit 1 2014-2015
Systematic errors
4
Determination of error
o
Accuracy
o
Precision
Evaluating accuracy and precision in data
o
When evaluating whether data is accurate or precise you could look at
•
Single Data Point –
•
Set of Data Points -
CDO IB Chemistry SL/HL Trimble
Unit 1 2014-2015
Precision vs. accuracy
5
Uncertainties in calculated results
Significant figures in mathematical operations
o
Addition/Subtraction –
o
Multiplication/Division –
o
Mixed operations –
Example of Sig. Figs in Calculations
33.5 cm + 7.88 cm + 0.977 cm =
23000 km + 8.7 km =
67.23 cm x 9.22 cm =
Percent Uncertainties and errors
o
Fractional Uncertainty
o
Absolute Uncertainty –
• Example:
o
Percent Uncertainty
CDO IB Chemistry SL/HL Trimble
Percentage uncertainties and propagation of errors
Unit 1 2014-2015
200 cm x 3.333 cm =
6
Percent Uncertainties and errors
o
Percent Error
Error propagation
o
Error propagation is a way of
o
All chemical equipment has
Ex.
10.00mL pipettes
50.00mL burettes
Thermometer -
Rule: 1 Addition and Subtraction
o
Example
22.34 + 0.02 mL - 1.06 + 0.02 mL
Rule 2: Multiplication and Division
o
Make
o
Convert
o
Add
o
Multiply
o
Apply
=
Unit 1 2014-2015
If you add or subtract two numbers
CDO IB Chemistry SL/HL Trimble
o
7
Example: Multiplication and Division
o
Find the density of a substance using the following data:
g = 1.22 + 0.01 g
V = 21.28 + 0.04 mL
Example: multiplying and dividing
1. Density =
2. Converting Uncertainties to Percent Uncertainties

Mass:

Vol:
Example: multiplying and dividing
3. Adding percent uncertainties
Rule 3: Whole number
•
Multiplying or dividing by a whole number –
Example:
4.95 ± 0.05 x 10
CDO IB Chemistry SL/HL Trimble
5. Report Value with Propagated Error
Unit 1 2014-2015
4. Multiply Percent Uncertainty by Calculated Value
8
Rule 4: Powers
o
Powers -
Example:
(4.3 ± .5 cm)3
Rule 5: Formulas
Unit 1 2014-2015
Formulas - Follow the order of operations:
CDO IB Chemistry SL/HL Trimble
o
9
CDO IB Chemistry SL
Problem Set 1-1
1. Determine the number of significant figures in each of the following numbers.
a. 175,000
b. 0.0125
c. 76,000
d. 0.4600
e. 0.00000000525
f. 900
g. 900.
h. 10,100
i. 0.07007
2. Round off each of the following numbers to three significant figures
a. 15.9994
b. 1.0080
c. 0.6654
d. 4885
e. 87,550
f. 0.027225
CDO IB Chemistry SL/HL Trimble
4. How many significant figures are in each of the following numbers?
a. 225.0
b. 1000.0
c. 0.0003210
d. 0.0067
e. 1,000,000.
f. 2.00001
Unit 1 2014-2015
3. Put the following numbers into scientific notation and write down the number of significant digits
in each:
a. 0.225
b. 2.5
c. 44,163
d. 20,190
e. 0.00000000000991
f. 7,000
10
CDO IB Chemistry SL
Problem Set 1-2
1. Perform the indicated arithmetic operations, and round the results to the appropriate number of
significant digits.
a. 77.981 x 2.33 =
b. 4 x 0.0665 =
c. 17.34 + 4.900 + 23.1 =
d. 9.80 – 4.762 =
e. 3.9 X 6.05 X 420 =
f. 14.1 / 5 =
g. 1001 + 16.23 =
h. 424.5 + 2.8461 =
i. 9.9 – 9.54 =
9
10
j. 7.3778 – 0.000265 =
k. 8.561 x 10 – 6.21 x 10 = l. (24.358)(6.4) =
m. 48.6(0.6959) =
n. 23081 / 0.8981 =
o. (6.082 x 1023)(5.0 x 10-3) =
4
2
p. (9.9x10 ) + (1.273 x 10 ) =
2. In the diagram at right, 4 targets are shown. If the goal is to hit the centre of the bulls-eye,
a. Which show a precise aim?
b. Which show an accurate aim?
3. a) Calculate the average and the uncertainty for each set of data:
b) The "true" value that we were attempting to measure was: 16.26
Which set of data is most precise? _______ Which was most accurate? _______
4. In an experiment, you are measuring the mass of water by difference. You use only one
balance, but ask 2 friends to help you make measurements. Your data looks like this:
You
Friend A
Friend B
Avg. with Uncertainty
Empty Beaker
207.2 g
207.1 g
207.3 g
Beaker + 50mL
257.3 g
257.0 g
257.5 g
water
50 mL water alone
Complete the table. Might random error be present? What is causing it? If so, how would you
correct for it? Might systematic error be present? What is causing it? How would you find out?
Unit 1 2014-2015
UNCERTAINTY
CDO IB Chemistry SL/HL Trimble
AVERAGE
SET A: 15.32, 15.37, 15.33, 15.38, 15.35
SET B: 16.30, 16.19; 16.24 16.29, 16.23
11
CDO IB Chemistry SL
Problem Set 1-3
1. Adding and subtracting values:
a) 1.00 + 0.05 g of Copper is added to 10.00 g+ 0.05 g of Iron. What is the mass of the two,
together?
b) The starting volume on a buret is 40.00 + 0.02 mL. The final volume on the buret is 32.60 + .02
mL. What volume of liquid was removed from the buret?
c) The weighing boat weighs 2.45 + 0.01 g. The total weight, after adding Calcium Carbonate to
the weighing boat is 4.62 + 0.01 g. What is the mass of the calcium carbonate?
2. Multiplying and dividing when both values have uncertainty
a) Molarity: Calculate the molarity when 2.0 + .1 moles of NaCl is dissolved in 0.100 + 0.001 L
of water. ( Molarity = moles / L )
b) Density: Calculate the density of an object with mass 25.0 + .2 g and volume 50.0 + .5 mL
(Denisty = mass/volume)
c) Density: Calculate the density of a rectangular object with mass 32.0 + .2 g, length 1.25 + .05
cm, width 2.25 + .05 cm and height 3.35 + .05 cm.
CDO IB Chemistry SL/HL Trimble
Unit 1 2014-2015
3. Other Rules:
a) 13.62 + 0.02 cm x 100
b) Find the volume of a rectangle measuring
l: 2.5 + 0.1cm w:4.2 + 0.1cm h:1.1 + 0.1 cm
c) (3.6 + 0.5 cm)3
12