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Significant Digits/Figures
Sept. 2, 2014
SIGNIFICANT FIGURES OR DIGITS
• THE NUMBER OF SIGNIFICANT FIGURES
INCLUDED IN A CALCULATION OR
MEASUREMENT IS DEPENDENT ON THE
ACCURACY OF THE MEASURING DEVICE
OR INSTRUMENT USED TO MAKE THE
ORIGINAL MEASUREMENTS
Exact v. Inexact Numbers
• Exact numbers – those numbers known
exactly (by definition or by counting)
– One dozen = 12, one inch = 2.54 cm, 33
students in the room
• Inexact numbers – values with some
uncertainty; anything measured using a piece
of equipment (balance, graduated cylinder)
– Mass of penny = 3.03 grams
Precision v. Accuracy
• Precision – a measure of how closely
individual measurements agree with
one another (repeatability)
– A balance is precise if it gives you the same
value for every trial
• Accuracy – how closely individual
measurements agree with the correct or
“true” value (bullseye)
– a balance is considered more accurate with
increasing decimal places (+/- 0.0001 g is
more accurate than +/- 0.01 g)
– Greater accuracy of an instrument means
more significant figures.
SIGNIFICANT FIGURES
• RULE 1: Digits other than zero are always
significant.
Examples:
96g
61.4g
0.52g
2 significant digits
3 significant digits
2 significant digits
SIGNIFICANT FIGURES
• RULE 2: One or more final zeros used after the
decimal point are always significant (determined by
the accuracy of the measuring device: i.e. - balance
or electronic balance, etc.)
Example:
4.72 km
4.7200 km
82.0 m
3 significant digits
5 significant digits
3 significant digits
SIGNIFICANT FIGURES
• RULE 3: Zeros between two other
significant digits are always significant.
Example:
5.029 m
306 km
6.02 x 10²³ particles
4 significant digits
3 significant digits
3 significant digits
SIGNIFICANT FIGURES
• RULE 4: Zeros used solely for spacing the
decimal point are not significant. The zeros
are place holders only.
– You can tell a number is a placeholder if when you
remove the zeros, the number CHANGES its value
Example:
7000 g
0.00783 kg
1 significant digit
3 significant digits
SIGNIFICANT FIGURES
• RULE 5: Counting numbers and defined
constants have and infinite number of
significant digits
Summary
• SIGNIFICANT DIGITS: digits that represent
actual measurements.
1. Digits other than zero.
2. Zeros after the decimal.
3. Zeros in the middle of significant
digits.
You Try!
• How many sig figs in the following:
Number of Significant Figures:
Examples:
a) 4
a) 1001 km
b) 4
b) 34.00 m
c) 5
c) 129,870 m
d) 1
d) .003 km
e) 4
e) 1.003
f) 5
f) .0072561 g
g) 1
g) 20,000 cm
h) 2
h) .0023 g
CALCULATIONS WITH SIG FIGS
• RULE: When multiplying or dividing
measurements, round off the final answer to the
number of significant digits in your
measurement having the least number of
significant digits
Examples:
1. 2.03 cm x 36.00 cm = 73.08 cm²
= 73.1 cm²
2. (1.13 m)(5.126122m) = 5.7925178 m²
= 5.79 m²
3. 49.6000 cm² / 47.40 cm = 1.0464135 cm
= 1.046 cm
CALCULATIONS WITH SIG FIGS
• RULE: For addition and subtraction, the answer
may contain only as many decimal places as the
measurement with the least number of decimal
places.
Examples:
1) 677.1 cm
39.24 cm
+ 6.232 cm
722.572 cm
= 722.6 cm
2) 34.231 g
3) 16.45 cm
6.709 g
- 8.329 cm
+ 18.20 g
8.121 cm
59.140 g
= 8.12 cm
= 59.14 g
You Try!
• Addition
165.5 cm + 8 cm + 4.37 cm =
• Multiplication
2.6 cm x 3.78 cm =
You Try!
• Addition
165.5 cm + 8 cm + 4.37 cm = 177.87 cm
= 178 cm
• Multiplication
2.6 cm x 3.78 cm = 9.828 cm2
= 9.8 cm2