Significant Figures Essay example

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Pages: 4

Techniques Lab

Lab Notebook
• See pages 10-11
• Required Headings for each lab:
o Title
o Purpose (2-3 sentences briefly stating main concepts, reactions and techniques)
o Theory (1-2 pages outlining relevant theory of concepts, reactions and techniques.
Chemical structure, figures and schematic diagrams are highly recommended.)
o Procedure (A point form version of experimental procedure. Tables for data collection
are required.)
o Chemical Hazards (Toxicological properties, preventative measures, first aid measures)

• Write in pen
• Write on the original page and insert divider under
copy sheet before wiring
• Put your name on the front and leave room for a Table
of Contents

Determinate and
Indeterminate Errors
• Determinate errors: systematic, experimental
o i.e. inaccurate equipment, impure reagents

• Indeterminate errors: operator, random
o i.e. Losses from transfers, differences in judgement

Precision versus Accuracy
Precision:
agreement
between various
measurements
Accuracy:
agreement
between the
average result and
the actual value

http://celebrating200years.noaa.gov/magazine/tct/accuracy_vs_precision.html 2010-09-14

Uncertainty
• There is always some uncertainty in measurement
• Equipment in this lab has typical uncertainty
o See page 43

Instrument

Typical Uncertainty

Graduated cylinder, 10 mL

± 0.1 mL

Graduated cylinder, 100 mL

± 0.2 mL

Pipette, 5 mL

± 0.01 mL

Pipette, 10 mL

± 0.02 mL

Pipette, 25 mL

± 0.03 mL

Balance: Electronic top loader

± 0.01 g

Balance: analytical, Mettler
AE160/AE200

± 0.0001 g

Significant Figures
• Significant figures help to identify the precision of a
measurement
o Zeros to denote position of decimal are not sig figs

Number of sig figs

Number of sig figs

0.0301 g

3

0.001030 g

4

4.290 hours

4

5000 miles

1 (but ambiguous)

1.030 mg

4

5.000 x103
miles

4

• Example: using a 10 mL graduated cylinder, measured
6.2 mL
o According to the typical uncertainty in equipment, the data would be
recorded as 6.2 ± 0.1 mL
o 2 sig figs in the measurement
o 6 is certain, 2 is uncertain

Significant Figures in
Calculations
• Addition and Subtraction:
o Significant figures should be reported to the precision of the term of lowest
precision
24.35
- 9.575
+11.2
+0.46
26.435 -> 26.4 (3 significant figures)
Note: Keep the least decimal places
o Perform the calculation and then round off the digits

Significant Figures in
Calculations
• Multiplication and Division
o Significant figures are reported to the precision of the term of lowest
relative precision



ସଷ଻.଺଼ଽ ×ହ.ଶ
ସ.଴ଷ

= 5.648 × 10ଶ → 5.6 × 10ଶ

Note: Keep the least sig.fig.

(2 sig figs)

Significant Figures in
Calculations
• Logarithms and Antilogarithms
o The number of sig fig. in the number = The number of decimal places in
the logarithm
o For example:

log 1.21
3 sig. figs

=
0.083
- 3 decimal places

o In pH calculations
if [H+] = 0.047M, pH = -log 0.047 (2 sig. figs)
= -log 4.7x10-2
= 2.00 - log 4.7
= 2.00 - 0.67(2)
= 1.33 (2 decimal places)

Significant Figures in
Calculations
• Multistep calculations:
o Calculate intermediate results beyond the necessary precision and round
off at the end

• Rounding:
o If the figure next to the last retained digit is 5 or more round up
o If the If the figure next to the last retained digit is lee than 5 round down
o 4.6349
o 4.6349

4.635 (to 4 sig figs)
4.63 (to 3 sig figs)

Uncertainty in
Calculations
• Addition and Subtraction
o Uncertainty is the sum of the uncertainties of each component
measurement

• Length measurement
o Between 1.38 ± 0.02 cm and 13.85 ± 0.02 cm
13.85
- 1.38
12.47

± 0.02
± 0.02
± 0.04 cm

• Uncertainty of the Average
o Three trials of a length measurement:(1)18.50 ± 0.04 cm; (2)18.40 ± 0.04
cm; (3)18.60 ± 0.04 cm
o Average : (18.50 +18.40…