SNC2D1: Notes
Significant Digits
When reporting values that were the result of a measurement or
calculated using measured values, it is important to have a way to
indicate the certainty of the measurement. This is accomplished
through the use of significant figures.
Significant figures are the
digits in a value that are known with some degree of confidence.
As
the number of significant figures increases, the more certain the
measurement. As precision of a measurement increases, so does the
number of significant figures.
There are conventions that must be followed for expressing numbers
so that their significant figures are properly indicated. These
conventions are:
1. If a decimal point is present, zeros to the left of the first nonzero digit (leading zeros) are not significant. E.g. 0.03 has
one significant digit and 0.000450 has three significant digits.
2. If a decimal point is not present, Zeros to the right of the
last non-zero digit (trailing zeros) are not significant. E.g. 50
m has one significant digit and 5500 s has two significant
digits.
3. All digits included in a stated value (except leading and trailing
zeros) are significant digits.
4. When a measurement is written in scientific notation, all digits
in the coefficient are significant. E.g. 3.5 x 108 has two
significant digits and 2.56 x 1018 has 3 significant digits.
See table below for further examples
Table 1 Certainty of Measurements
Measurement
Certainty
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307.0 cm
4 significant
digits
61 m/s
2 significant
digits
0.03 m
1 significant
digit
0.5060 km
4 significant
digits
3.00 x 108
3 significant
m/s
digits
6400 s
2 significant
digits
Table 1.1 Examples of Significant Digits
EXAMPLES
# OF SIG. DIG.
453 kg
3
5057 L
4
COMMENT
All non-zero digits
are always significant.
Zeros between 2 sig.
dig. are significant.
Additional zeros to
5.00
3
the right of decimal
are significant.
0.007
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1
Placeholders are not
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significant.
 How many significant digits are there in these numbers?
i)
3805.0 cm
ii)
28 m/s
iii)
0.00036015 mg
iv)
0.05000 cm3
Rules When Doing Calculations
Multiplication and Division
RULE: When multiplying or dividing, your answer may only show as
many significant digits as the multiplied or divided measurement
showing the least number of significant digits.
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Example: When multiplying 22.37 cm x 3.10 cm x 85.75 cm =
5946.50525 cm3
We look to the original problem and check the number of significant
digits in each of the original measurements:
22.37 shows 4
significant digits.
3.10 shows 3 significant
digits.
85.75 shows 4
significant digits.
Our answer can only show 3 significant digits because that is the
least number of significant digits in the original problem.
5946.50525 shows 9 significant digits, we must round to the
tenth place in order to show only 3 significant digits. Our final
answer becomes 5.95 x 103 cm3.
Adding and Subtracting
RULE: When adding or subtracting your answer can only show as many
decimal places as the measurement having the fewest number of
decimal places.
Example: When we add 3.76 g + 14.83 g + 2.1 g = 20.69 g
We look to the original problem to see the number of decimal places
shown in each of the original measurements. 2.1 show the least
number of decimal places. We must round our answer, 20.69, to
one decimal place (the tenth place). Our final answer is 20.7 g
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Note: We will not be applying this rule in the optics unit.
SCIENTIFIC NOTATION

Scientific notation is generally used for numbers smaller that 0.1
and larger than 99.

In scientific notation, a number has the form X x 10n, where X
is greater than or equal to 1 but less than 10, and 10n is a
power of 10. In other words 102 = 10 x 10, while 104 = 10 x
10 x 10 x 10
Example – 1
Place the following numbers into scientific notation
58 000 000
The decimal point is located here. Move
the decimal 7
places to the left
5.8 000 000
Convert your answer in the form
X x 10n.
5.8 x 107
Example – 2
0.00000000053
To convert this number into scientific
notation move the decimal
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point 10 places to the right so that you have a
number greater
than zero to the left of the decimal.
5.3 x 10-10
Note: That when the decimal point is moved to the left, the
exponent is positive and when the decimal point is moved to the
right the exponent is negative.
Scientific Notation & Your Calculator
To enter a number such as 1.2x10-3 into your calculator:
-
enter 1.2
-
press the EXP or EE button. Many calculators show this as:
1.2
-
00
press the +/- but
1.2
-00
-
press 3
1.2
-03
You should practice entering numbers in scientific notation rather
than converting them into non-scientific notation
Answer the following. Ensure that your answer has the appropriate
number of significant digits
a) 36.0 cm x 2.5476 cm =
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b) 2.1 m x 3.7 m =
c) 0.0245 x 38.69 =
d) 6.25 cm3 x 0.030057 cm3
e) 10.0 km / 6km =
Remember These Rules:
1. Digits from 1-9 are always significant.
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2. Zeros between two other significant digits are always
significant
3. One or more additional zeros to the right of both the decimal
place and another significant digit are significant.
4. Zeros used solely for spacing the decimal point (placeholders)
are not significant.
Instructions: Identify the number of significant digits show in each of
the following examples.
1)
400
2)
200.0
5) 320
6)
0.00530 7)
Answers: 1) 1
5
8) 6
9)
103
4.0 x
2) 4
10)
1.67 x
10-8
13) 635.000 14)
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3) 1
3)
4) 3
11)
0.0001
15)
218
22 568 8) 4755.50
5) 2
5 x
1012
22 000
4)
6) 3
7)
12)
2.00 x
104
5201
16)
81
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Answers: 9) 2
10) 3
2
15) 4
16) 2
11) 1
12) 3
13) 6
14)
RULE: When multiplying or dividing, your answer may only show as
many significant digits
as the multiplied or divided measurement showing the
least number of significant
digits.
Instructions: Perform the following calculations and round according
to the rule above.
1)
13.7 x 2.5 =
2)
200 x 3.58
=
4)
=
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5003 / 3.781
5)
3)
0.00003 x 727
=
89 / 9.0
6)
5000 / 55 =
=
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Answers:
1) 34
2) 7x102
5) 9.9
6) 9x101
1)
50.0 x 2.00
=
4)
2)
3) 0.02
2.3 x 3.45 x 3)
4) 1323
1.0007 x 0.009 =
7.42 =
51 / 7 =
5)
208 / 9.0
6)
0.003 / 5 =
=
Answers 1) 1.00x102
2) 59 3) 0.009
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4) 7
5) 23
6)
0.0006
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