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Department of Engineering Education
Fall 2005
Page 1 of 6
Virginia Polytechnic Institute and State University
Copyright:
J. C. Malzahn Kampe, 2004, 2005
Significant Figures Supplement
EngE 1024
First, let’s look at the definitions of four basic terms that will be used in this document.
significant figures – in a number, the digits beginning with and including the leftmost nonzero
digit and ending with the digit in the decimal place to the right that contains the first occurrence
of uncertainty.
Examples (digits with an “s” above are significant, those with “n” are not):
n.nnssss
s.ss x nn
n
sss.s
sss
ss?
0.003070
2.00 x10
4
700.0
241
120 (see page 2)
placeholder zero – a zero digit that is used only to place the decimal point in the proper place
and the significant figures in their proper value columns (e.g., ones place, tenths place).
Place
holder zeros are not significant figures.
Examples (zeros with “p” above are placeholders, those with “s” are significant figures):
n.ppssss
s.ss x np
n
sss.s
sss
ss?
0.003070
2.00 x10
4
700.0
241
120 (see page 2)
This is a “leading zero.”
It is not a significant figure,
but it is not a placeholder
zero either.
accuracy – the closeness of a measured value to the true value for the quantity being
measured.
precision – in replicate testing (running the same test many times), precision is “repeatability” or
the closeness of the measured values
to each other
– which is not the same as closeness to
the true value for the quantity.
In a single test, precision is how closely the measurement
reading can be made, which is usually half of the smallest division that can be read on the scale
of the instrument.
Significant figures tell you how precisely a value is measured – they have nothing to do
with accuracy.
Let’s look at an example.
Suppose you have a scale that measures mass in
kilograms and the zero on the scale has not been set properly, hence all readings are “off” by
one kilogram.
Now, let’s say that you use the scale to measure your mass.
You report your
mass as 64.1 kg, which reflects the precision with which your scale can be read (one half of the
smallest scale division).
The use of three significant figures, the last of which falls in the tenths
place, implies only that you are able to read the scale to
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This note was uploaded on 10/02/2008 for the course ENGE 1024 taught by Professor Dcohanehi during the Fall '06 term at Virginia Tech.
 Fall '06
 DCOhanehi

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