Significant Figures

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How much is Bill Gates worth?
$61 BILLION
Question: is that EXACTLY
$61, 000,000,000.00?????
Significant Figures
1
Significant Figures
A measurement is always limited by the precision of the
Instrument. An understanding of significant figures is
important to express the appropriate precision of a
measurement
• Only zeros are non-significant digits (but not all always)
• There are cases where a zero may be significant:
1. A Zero between 2 non-zeros digits. (103 cm)
2. Numbers less than 1, Zeros in front of the first non
zero digit are not significant. (after start counting, they
are significant)
0.002030 km (the last zero indicates measurement has
been made that far out).
3. Numbers greater than 1, Zeros at the end of numbers
do not refer to a precise count
980000 (There are exceptions: decimal points, bar over)
2
Significant Figures
• 0.004070 -- The zeros shown in red are not significant.
The number is precise to 4 significant digits
• With numbers having a zero at the end the number of
significant figures depends on the precision with which the
number is known (how far was it measured).
• 40000 -- one significant digit. The number is known to the
nearest
ten thousand.
_
• 40000 -- three significant digits. The number is known to the
nearest
_ hundred.
• 40000 -- five significant digits. The number is known to the
nearest unit.
3
Significant Figures
Practice: # of sig figs
• 101
• 200
• 100.00
• 0.0008
• 0.005600 _
• 30 780 000
• 30 780_ 000
• 30 780 000
Answers:
3
1
5
1
4
8
4
5
4
Scientific Notation
• Large numbers are hard to visualize. Scientific
notation writes numbers in two parts:
– a number between 1 and less than 10 and
– a power of 10
• Examples
• 30 000 000 is represented as 3 x 107
• 0.0000482 is represented as 4.82 x 10-5
• Note: The numbers present in Sci. Not. are
SIGNIFICANT!!!
5
Scientific Notation
Practice:
• 0.0065
• 21 500
• 0.1408
• 589420
• 0.000 000 000 1
• 20 000 000 000 000 000
Answers:
• 6.5 x 10-3
• 2.15 x 104
• 1.408 x 10-1
• 5.8942 x 105
• 1 x 10-10
• 2 x 1016
6
Significant Figures
• Math Functions:
Addition/subtraction:
• When adding or subtracting, answer will have FEWEST decimal
places.
– Dumb People Are Stupid
Multiplying/dividing:
• When multiplying or dividing, answer with fewest Sig. Figs.
– My Dad Sells Fireworks
7
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