Transcript Significant Figures and Calculations

Significant Figures…
Bluefield High School
1
What is a significant digit?
Significant digits is a set of internationally accepted
rules for measurement.
The rule of thumb is to record all digits that are
certain, plus one that is estimated.
The rules of significant digits apply to all reporting
and calculating unless you are dealing with defined
values (those by definition. For example …60
minutes = 1 hour).
The Rules of Significant Digits…
 1. Every nonzero digit is significant. 24.7 has three significant digits
 2. Zeroes between nonzero digits are significant. 2.07m and 109m
each have three significant digits.
 3. Zeroes in front of all nonzero digits are not significant. They are
merely place holders. The measurements of 0.00037m and 0.46m
each have two significant digits.
 4. Zeroes at the end of the number and to the right of the decimal
point are significant. The measurement 43.00m, 1.010m and
9.500m all have four significant digits.
 5. Zeroes at the end of a measurement and to the left of the decimal
point are unclear. You may consider all such zeroes to be not
significant. To avoid confusion, express the number in scientific
notation.
When to use Significant figures
When a measurement is
recorded only those digits that
are dependable are written
down.
When to use Significant digits…
 If you measured the width of a
paper with your ruler you might
record 21.7cm.
To a mathematician 21.70, or
21.700 is the same.
But, to a scientist 21.7cm and
21.70cm is NOT the same
 21.700 cm to a scientist means the
measurement is accurate to
within one thousandth of a cm.
 significant figures video
How many sig digits?
7
40
0.5
0.00003
7 x 105
7,000,000
1
1
1
1
1
1
How many sig digits here?
1.2
2100
56.76
4.00
0.0792
7,083,000,000
2
2
4
3
3
4
How many sig digits here?
3401
2100
2100.0
5.00
0.00412
8,000,050,000
4
2
5
3
3
6
Counting Significant Figures
Number of Significant Figures
38.15 cm
5.6 ft
65.6 lb
122.55 m
4
2
___
___
All non-zero digits in a measured number are
(significant or not significant).
10
Leading Zeros
Number of Significant Figures
0.008 mm
1
0.0156 oz
3
0.0042 lb
____
0.000262 mL
____
Leading zeros in decimal numbers are
(significant or not significant).
11
Sandwiched Zeros
Number of Significant Figures
50.8 mm
3
2001 min
4
0.702 lb
____
0.00405 m
____
Zeros between nonzero numbers are
(significant or not significant).
12
Trailing Zeros
Number of Significant Figures
25,000 in.
2
200 yr
1
48,600 gal
3
25,005,000 g
____
Are trailing zeros, serving as place holders
in numbers without decimals, significant
or not significant?
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Learning Check
A. Which answer contains 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
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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
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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
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Solution …
3) 0.000015 and 150,000
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Learning Check
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
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Solution
A. 0.030 m
2
B. 4.050 L
4
C. 0.0008 g
1
D. 3.00 m
3
E. 2,080,000 bees
3
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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
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Adding and Subtracting
The answer has the same number of decimal places
as the measurement with the fewest decimal
places.
25.2
one decimal place
+ 1.34 two decimal places
26.54
answer 26.5 one decimal place
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Learning Check
In each calculation, round the answer to the
correct number of significant figures.
A. 235.05 + 19.6 + 2.1 =
1) 256.75
2) 256.8
3) 257
B. 58.925 - 18.2 =
1) 40.725
2) 40.73
3) 40.7
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Solution
A. 235.05 + 19.6 + 2.1 =
2) 256.8
B. 58.925 - 18.2
3) 40.7
=
23
Multiplying and Dividing
Round (or add zeros) to the calculated
answer until you have the same number of
significant figures as the measurement
with the fewest significant figures.
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Learning Check
A. 2.19 X 4.2 =
1) 9
B. 4.311 ÷ 0.07 =
1) 61.58
C.
2) 9.2
3) 9.198
2) 62
2.54 X 0.0028 =
0.0105 X 0.060
1) 11.3
2) 11
3) 60
3) 0.041
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Solution
A.
B.
C.
2.19 x 4.2
=
4.311 ÷ 0.07 =
2) 9.2
2.54 x 0.0028 =
0.0105 x 0.060
2) 11
3) 60
Continuous calculator operation =
2.54 x 0.0028  0.0105  0.060
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Significant Figures
Multiplication or Division
The number of significant figures in the result is set by the original
number that has the smallest number of significant figures
4.51 x 3.6666 = 16.536366 = 16.5
3 sig figs
round to
3 sig figs
6.8 ÷ 112.04 = 0.0606926 = 0.061
2 sig figs
round to
2 sig figs
1.8
Accuracy – how close a measurement is to the true value
Precision – how close a set of measurements are to each other
accurate
&
precise
precise
but
not accurate
not accurate
&
not precise
1.8
Scientific Notation
A short-hand way of writing
large numbers without
writing all of the zeros.
The Distance From the Sun to
the Earth
93,000,000
Step 1
 Move decimal left
 Leave only one number in front of decimal
Step 2
 Write number without zeros
Step 3
 Count how many places you moved decimal
 Make that your power of ten
The power of
ten is 7 because
the decimal
moved 7 places.
93,000,000 --Standard Form
9.3 x 107 ---
Scientific Notation
Practice Problem
Write in scientific notation.
Decide the power of ten.
98,500,000 = 9.85 x 10?
2) 64,100,000,000 = 6.41 x 10?
3) 279,000,000 = 2.79 x 10?
4) 4,200,000 = 4.2 x 10?
1)
9.85 x 107
6.41 x 1010
2.79 x 108
4.2 x 106
More Practice Problems
On these, decide where the decimal will be moved.
1)
2)
3)
734,000,000 = ______ x 108
870,000,000,000 = ______x 1011
90,000,000,000 = _____ x 1010
1) 7.34 x 108
2) 8.7 x 1011
3) 9 x 1010
Complete Practice Problems
Write in scientific notation.
1)
2)
3)
50,000
7,200,000
802,000,000,000
1) 5 x 104
2) 7.2 x 106
3) 8.02 x 1011
Scientific Notation to Standard
Form
Move the decimal to the right
3.4 x 105 in scientific notation
3.40000 --- move the decimal
340,000 in standard form
Write in Standard Form
 6.27 x 106
 6,270,000
 9.01 x 104
 90,100
 tutorial
Dimensional Analysis Method of Solving Problems
1. Determine which unit conversion factor(s) are needed
2. Carry units through calculation
3. If all units cancel except for the desired unit(s), then the
problem was solved correctly.
How many mL are in 1.63 L?
1 L = 1000 mL
1000 mL
1.63 L x
= 1630 mL
1L
2
1L
L
1.63 L x
= 0.001630
1000 mL
mL
1.9
The speed of sound in air is about 343 m/s. What is
this speed in miles per hour?
meters to miles
seconds to hours
1 mi = 1609 m
1 min = 60 s
1 mi
60 s
m
x
x
343
s 1609 m
1 min
1 hour = 60 min
60 min
mi
x
= 767
hour
1 hour
1.9
Please do the following questions…
 Page 349 in your text…
#’s 2,3,4,5,6,8 and 9
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