Transcript Significant Figures PPT

Motion Unit
Measurements
Significant Figures in
Calculations
“A man with a watch knows
what time it is. A man with two
watches is never sure”
(Unknown)
I weigh some sugar on my kitchen scales and
some more sugar on my lab balance. The results
are shown below. How much sugar should I say I
have, in total, without being misleading?
Kitchen scales: 2.2 kilograms
Lab scale: 101.237grams
(1kg = 1000g)
Significant Figures in
Measurement
It is important to be honest when
reporting a measurement, so that it
does not appear to be more accurate
than the equipment used to make the
measurement allows. We can achieve
this by controlling the number of digits,
or significant figures, used to report the
measurement.
Significant Figures in
Measurement
 The numbers reported in a measurement
are limited by the measuring tool
Significant Figures
• Significant figures are the meaningful figures
in our measurements and they allow us to
generate meaningful conclusions
• Numbers recorded in a measurement are
significant.
– All the certain numbers plus first estimated
number
–
e.g. 2.85 cm
• We need to be able to combine data and still
produce meaningful information
Where we are going….
3.54 + 3.4
Counting Significant Figures
All non-zero digits in a measured number are ALWAYS
significant.
Number of Significant Figures
38.15 cm
5.6 ft
65.6 lb
122.55 m
Sandwiched Zeros
Complete: Zeros between nonzero numbers
are ALWAYS significant
Number of Significant Figures
50.8 mm
2001 min
0.702 lb
0.00405 m
Leading Zeros
All zeros to the left of the first non-zero (leading zeros in decimal
numbers) are not significant.
Number of Significant Figures
0.008 mm
0.0156 oz
0.0042 lb
0.000262 mL
Trailing Zeros
If there is a decimal, zeros to the right of the last non zero
are ALWAYS significant (trailing zeros in numbers without
decimals are significant if they are serving as place holders).
Number of Significant Figures
25.000 in.
20.0 yr
48.600 gal
20 005 000. 00 g
Trailing Zeros
It is difficult to decide significance of zeros to the right of
non zero digits in a number without a decimal. This
depends on the instrument used. A line or decimal is
often used to identify significance.
Otherwise if there is no decimal they are not significant.
Number of Significant Figures
25 000 in.
200 yr
48.600 gal
20 005 000 g
Learning Check
A. Which answers contain 3 significant
figures?
1) 0.4760
2) 0.00476
3) 4760
B. All the zeros are significant in
1) 0.00307
2) 25.300
3) 2.050 x 103
C. 534,675 rounded to 3 significant figures is
1) 535
2) 535,000
3) 5.35 x 105
Solution
A. Which answers contain 3 significant
figures?
2) 0.00476
3) 4760
B. All the zeros are significant in
2) 25.300
3) 2.050 x 103
C. 534,675 rounded to 3 significant figures is
2) 535,000
3) 5.35 x 105
Learning Check
In which set(s) do both numbers contain
the same number of significant figures?
1) 22.0 and 22.00
2) 400.0 and 40
3) 0.000015 and 150,000
Solution
In which set(s) do both numbers contain
the same number of significant figures?
3) 0.000015 and 150,000
Learning Check SF3
State the number of significant figures in
each of the following:
A. 0.030 m
1
2
3
B. 4.050 L
2
3
4
C. 0.0008 g
1
2
4
D. 3.00 m
1
2
3
E. 2,080,000 bees
3
5
7
Solution
A. 0.030 m
2
B. 4.050 L
4
C. 0.00008 g
1
D. 3.00 m
3
E. 2,080,000 bees
3
Significant Numbers in
Calculations
 A calculated answer cannot be more
precise than the measuring tool.
 A calculated answer must match the least
precise measurement.
 Significant figures are needed for final
answers from
1) adding or subtracting
2) multiplying or dividing
Adding and Subtracting
The answer has the same number of
decimal places as the measurement with
the fewest decimal places.
25.2
3 sig figs (one decimal places)
+ 1.34 3 sig figs (two decimal places)
26.54
answer 26.5 one decimal place
Solution
A.
2.19 X 4.2
B. 4.311 ÷ 0.07
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