10/6/11
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Significant Figures
When writing a number, it is important to
know how well the value of the number is
known.
Examples
If I say I have 12 donuts, I usually mean I
have exactly 12 donuts because donuts do
not come in fractions of a unit.
Significant Figures
If I say I have 12 grams of salt, does that
mean exactly 12 grams or something
between 11.5 and 12.5 grams.
Because the mass of an object in grams
may be expressed in fractions of grams, I
must specify as precisely as possible what
the mass is.
Significant figures indicate the precision with
which a number has been determined.
Significant Figures
When expressing a value, the number of
digits used indicates the number of digits
that could be measured accurately.
The final digit in the value is an estimate of
the least precise number.
4
6
5
Length = 5.73 units
Significant Figures
The manner in which a number is written
indicates the number of significant figures
it has.
Examples
4000
1 significant figure
the zeros are simply place holders and do
not indicate precision of the measurement.
in scientific notation: 4 x 10
3
Significant Figures
4000.
4 significant figures
By placing a decimal point after the last
zero, this indicates that the zeros were
measured
in scientific notation: 4.000 x 10
3
Significant Figures
4000.000
7 significant figures
zeros following the decimal point with no
other digits behind them also indicate
precision of measurement, so they count
as significant figures
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Significant Figures
.0004
1 significant figure
for numbers less than one, zeros following
the decimal point, but before the first digit,
are simply place holders and do not
indicate precision
in scientific notation: 4 x 10
4
Significant Figures
.000400 3 significant figures
zeros following digits in numbers less than
1 indicate precision and are significant.
in scientific notation: 4.00 x 10
4
Mathematical Rules for Significant
Figures
Addition/Subtraction
When adding or subtracting numbers, the
number of significant figures in the result is
determined from the position relative to the
decimal point of the least significant figure
of the numbers being added or subtracted
Because 472.1 has only
1 sig. fig. after the
decimal point, the final
answer can have only 1
sig. fig. after the decimal
point—the correct
answer is 5476.2
Mathematical Rules for Significant
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 Fall '09
 Scientific Notation, Accuracy and precision, experimental errors

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