First-Year Engineering Program
Significant Figures
This module for out-of-class study
only. This is not intended for classroom
discussion.
First-Year Engineering Program
Significant Figures
• Engineers often are doing calculations with
numbers based on measurements. Depending
on the technique used, the precision of the
measurements can vary greatly.
• It is very important that engineers properly
signify the precision of the numbers being
used and calculated. Significant figures is the
method used for this purpose.
First-Year Engineering Program
Accuracy vs. Precision
Accuracy refers to how closely a measured value
agrees with the true value.
Ex:
A scale to increments of 10 lbs is not very precise,
but, if it is well calibrated, it is accurate.
Courtesy: http://www.chem.tamu.edu/class/fyp/mathrev/mr-sigfg.html
First-Year Engineering Program
Precision vs. Accuracy
Precision refers to the level of resolution of the
number.
Ex:
A scale to increments of tenths of a gram has
good precision, however, if it is not well
calibrated, it would not be accurate.
A scale measures to 0.1 lbs is more precise
than one that measures to 1 lbs.
Courtesy: College Physics by A. Giambattista, B. Richardson and R.
Richardson
First-Year Engineering Program
Significant Figures and Precision
In engineering and science, a number representing a
measurement must indicate the precision to which the
measured value is known.
The precision of a device is limited by the finest
division on the scale.
Ex:
A meterstick, with millimeter divisions as the smallest
divisions, can measure a length to a precise number of
millimeters and estimate a fraction of a millimeter between
two divisions.
Courtesy: College Physics by A. Giambattista, B. Richardson and R. Richardson
First-Year Engineering Program
Significant Figures
The precision of a quantity is specified by the correct
number of significant figures.
Significant figures: All the digits that are measured or
known accurately plus the one estimated digit.
Ex:
d= 12 km (d is 12 km to the nearest kilometer-2
significant fig.)
d= 12.0 km (d is 12 km to the nearest tenth of a
kilometer-3 significant figures-MORE PRECISE)
More significant figures mean greater precision!!!
Courtesy: College Physics by A. Giambattista, B. Richardson and R.
Richardson
First-Year Engineering Program
Rules for Identifying Significant Figures
 Nonzero digits are always significant.
Ex: 58 - 5 and 8 are significant: 2 significant fig.
 Final or ending zeros written to the right of the decimal point
are significant.
Ex: 58.00 - 5, 8, and zeros are significant: 4 significant fig.
 Zeros written on either side of the decimal point for the purpose
of spacing the decimal point are not significant.
Ex: 0.058 - 5 and 8 are significant - 2 zeros are insignificant:
2 significant fig.
 Zeros written between significant figures are significant.
Ex: 30.058 - 3, 5, 8 and zeros are significant: 5 significant fig.
Courtesy: College Physics by A. Giambattista, B. Richardson and R. Richardson
First-Year Engineering Program
Exact Numbers
Exact numbers: Numbers known with complete certainty.
Exact numbers are often found as conversion factors or
as counts of objects.
Exact numbers have an infinite number of significant
figures.
Ex:
Conversion factors : 1 foot = 12 inches
Counts of objects: 23 students in a class
Courtesy:
http://www.chem.sc.edu/faculty/morgan/resources/sigfigs/sigfigs4.html
First-Year Engineering Program
Addition and Subtraction
of Significant Figures
When quantities are added or subtracted, the number of
decimal places (not significant figures) in the answer
should be the same as the least number of decimal
places in any of the numbers being added or subtracted.
Ex:
50.67 J
(2 decimal places - 4 significant fig.)
0.1 J
(1 decimal place - 1 significant fig.)
+ 0.9378 J
(4 decimal places - 4 significant fig. )
51.7078 J
(4 decimal places - 6 significant fig.)
Result: 51.7 J ROUNDING !!! (1 decimal place - 3 sig. fig.)
Courtesy: http://www.physics.uoguelph.ca/tutorials/sig_fig/SIG_dig.htm
First-Year Engineering Program
Multiplication, Division, etc.,
of Significant Figures
In a calculation involving multiplication, division,
trigonometric functions, etc., the number of significant
digits in the answer should be equal to the least
number of significant digits in any one of the
numbers being multiplied, divided etc.
Ex:
0.097 m-1 (3 decimal places - 2 significant fig.)
X 4.73 m
(2 decimal places - 3 significant fig. )
0.45881
(5 decimal places - 5 significant fig.)
Result: 0.46 ROUNDING !!! (2 decimal place - 2 sig. fig.)
Courtesy: http://www.physics.uoguelph.ca/tutorials/sig_fig/SIG_dig.htm
First-Year Engineering Program
Combination of Operations
In a long calculation involving combination of operations,
carry as many digits as possible through the entire set of
calculations and then round the final result appropriately.
DO NOT ROUND THE INTERMEDIATE RESULTS.
Ex:
(5.01 / 1.235) + 3.000 + (6.35 / 4.0)=
4.05668... + 3.000 + 1.5875=8.64418...
The first division should result in 3 significant figures. The
last division should result in 2 significant figures. In
addition of three numbers, the answer should result in 1
decimal place.
Result: 8.6 ROUNDING !!! (1 decimal place - 2 sig. fig.)
Courtesy: http://www.physics.uoguelph.ca/tutorials/sig_fig/SIG_dig.htm
First-Year Engineering Program
Combination of Operations
IF YOU ROUND THE INTERMEDIATE RESULTS:
Ex:
(5.01 / 1.235) + 3.000 + (6.35 / 4.0)=
4.06 + 3.000 + 1.6=8.66
If first and last division are rounded individually before
obtaining the final answer, the result becomes 8.7 which is
incorrect.
Courtesy:http://www.chem.sc.edu/faculty/morgan/resources/sigfigs/sigfigs4.html
First-Year Engineering Program
Sample Problems
PLEASE CHECK
PRACTISE:
THE
FOLLOWING
WEBSITES
TO
http://www.chem.sc.edu/faculty/morgan/resources/sigfigs/s
igfigs8.html
http://science.widener.edu/svb/tutorial/sigfigures.html
http://www.lon-capa.org/~mmp/applist/sigfig/sig.htm