Significant
Figures
Learning Objectives
• Learn the differences in:
– Accuracy/precision,
– Random/systematic error,
– Uncertainty/error
• Compute true, fractional, and percent error
• Use proper number of significant figures to
report work
Integer and Real Values

Real numbers represent continuous
quantities, e.g., length of rod, mass of rock,
velocity of a vehicle, etc.
L

Integer numbers represent discrete
quantities, e.g., number of marbles, number
of people, number of computers, etc.
Error
• Error can be associated with real and
integer values in measurements and
calculations.
• Engineers generally work with real
numbers.
Rat 7
Paired Jigsaw
• Front pair use Sig_Digits.ppt
• Back pair use Error.ppt
• Spend 10 minutes developing a 2-minute
summary of your handout (and giving
some examples)
• Spend 5 minutes exchanging 2-minute
summaries with the other half of your
team.
Team Exercise 7.1:
(3 minutes)
• The density of HCFC-22 (R-22 Freon) at
40oF was measured as 72.000 lbm/ft3.
• The actual (true) value is 79.255 lbm/ft3.
• Calculate:
– True error
– Fractional error
– Percent error
Team Exercise 7.2:
How “good” are these numbers (i.e., state
whether each reported number has a large
or small error)?
2 gallons
2.0001 gallons
5 billion people
100,393 people
600 pages
581 pages
100,000 ft2
128,462 ft2
Rules for Significant
Digits
• Combined operations:
– If using a calculator or computer,
perform the entire operation and then
round to the correct number of
significant digits.
• Sometimes, common sense and good
judgment is the only applicable rule!
Exact Conversions and Formulas
The number of significant digits in a final answer is not
affected by the number of digits in an exact conversion
factor or formula.
Examples:
• The exact conversion factor 12 in/ft is equivalent to 12.0000…in/ft
• The formula:
 * d2
Area 
4
is equivalent to
3.14159... * d2
Area 
4.00000...
Team Exercise 7.3
•
•
•
•
•
301.33 + 698. = ?
7.0700 / 30 = ?
70700 / 30.0 = ?
(-0.6643 + 0.00497)/1792 = ?
3.14/(693.3 - 693.27) = ?
Accuracy

Accuracy - nearness to the correct value.
Example:
A chemistry instructor makes a 5.00% sugar
solution. Using a sugar assay, a team of
students analyzes the solution and reports the
following results:
Student
Result
A
5.03%
B
4.96%
C
2.98%
Precision

Precision - repeatability of the measurement
indicates scatter in the data
Example:
A chemistry instructor makes a 5.00% sugar solution.
Using a sugar assay, a team of students analyzes the
solution in triplicate and reports the following results:
Student
Result
A
5.03%, 4.97%, 5.07%
B
4.49%, 5.52%, 5.01%
C
2.98%, 7.98%, 9.23%
Precision vs. Accuracy
Uncertainty
• Uncertainty results from random
error and describes lack of precision.
• Fractional Uncertainty =
Uncertainty
Best Value
• Percent Uncertainty =
Fractional Uncertainty * 100%
Team Exercise 7.4
• Compute the fractional and percent
uncertainty of a rod with a reported
length of 7.57 to 7.59 cm.