# SIGNIFICANT FIGURES (Sig. Figs.) by drr10525

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SIGNIFICANT FIGURES
(Sig. Figs.)

Significant = meaningful
A measurement can only be as accurate
and precise as the instrument that produced
it. A scientist must be able to express the
accuracy of a number, not just its
numerical value. We express the accuracy
of a number by the number of significant
figures it contains.
OBJECT

The object pictured above has an actual length. If we
were to measure its length, the reading we are allowed to
report would depend on the ruler that we used to make
the measurement. How many meaningful numbers
(Significant Figures) are recorded is limited by the ruler
markings.
On the ruler below we see markings for 0 and 10.
We have to make a guess at the units place. This
guess is significant. It would not make sense to
make a guess at the tenths place because we are
already unsure of the units place.

OBJECT

0                                                  10

A reading of 5 or 6 (one significant figure, one
guess) would be acceptable using this ruler.
On the ruler below, we see markings for 4, 5, 6, 7 etc.
We have to make a guess at the tenths place. This
guess is significant. It would not make sense to make
a guess at the hundredths place because we are already
unsure of the tenths place.

OBJECT

0    1     2    3     4    5     6    7     8    9    10

A reading of 5.2 or 5.3 (two significant figures, one sure
and one guess) would be acceptable using this ruler.
On the ruler below we see markings for .1, .2, .3, etc.
We have to make a guess at the hundredths place. This
guess is significant. It would not make sense to guess
at the thousandths place since we are already unsure of
the hundredths place.

OBJECT

0     1    2    3     4    5     6    7    8     9   10

A reading of 5.33 or 5.34 (three significant figures, two sure
and one guess) would be an acceptable reading using this ruler.
OBJECT

0   1   2   3    4   5   6   7   8   9   10

0   1   2   3    4   5   6   7   8   9   10

0                                         10
SIGNIFICANT FIGURES
In making measurements, one is allowed to record as
SIGNIFICANT FIGURES, all the numbers that are
represented by marks on the ruler (sure numbers), and
also one guessed/estimated number which falls in
between the last two marks on the ruler. No more
than one guess may be recorded as a significant
figure.
SIGNIFICANT FIGURES
ALL THE SURE NUMBERS AND ONE GUESS
thermometers.

68.4 deg C              -2.8 deg C              11.0 deg C

56.0 mL                4.34 mL                23.6 mL
Rules of Significant Figures
• All digits from 1 – 9 are significant.
• 23.55 has four Sig. Figs.
• Zeros between non-zero digits (captured)
are significant.
• 101 has three Sig. Figs.
• Zeros at the end of a number (Trailing
Zeros) are significant only if the number
contains a decimal point.
• 1,000,000. has seven Sig. Figs.
• 1,000 has only one Sig. Fig.
• 0.0250 has three Sig. Figs.
Rules of Significant Figures
• Zeros at the start of a number are considered
placeholders and are NOT significant.
• 0.000005 has only one Sig. Fig.
• Any number written in scientific notation only
displays those digits which are significant.
• 2.5 x 105 has 2 significant digits.
• Any number considered a constant has an
unlimited number of significant digits.
• The speed of light (c) = 3.0 x 108 m/s
How many significant figures are there in each of
the following measurements?

501 cm          three
501.0 mL        four
5000 mi         one
0.005 sec       one
0.1020 g        four
0.0203 lb       three
31.002 ºC       five
Calculations using Sig. Figs.
• Rounding: If the digit removed is less than 5, then
previous number will stay the same. If however it is equal
to or greater than 5, round the next digit up by one.
• Multiplication/Division: use the least number of Sig.
Figs. In the calculation.
• 5.2 x 10.3 = 53.56 = 54 (2 Sig. Figs.)
• Addition/Subtraction: use the least number of decimal
places in the calculation.
• 10.5 – 5.55 = 4.95 = 5.0 (only one decimal place)
• In Multi-step mathematical calculations: do all of the
math first and then go back and apply the sig. fig. rules.
• 25 x 4.00 – 15.5 = 84.5 = 85 (2 digits from the multiplication, no
decimal points from the subtraction)
THE END

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