physics (significant figures)
TRANSCRIPT
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THE NUMERICAL SIDE OF PHYSICS
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Objectives
1. Determine the number of significant figures in a numerical value.
2. Convert a number from normal notation to scientific notation
3. Use unit analysis to convert a measurement to another set of units
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Significant Figures
• the number of meaningful digits in a measured or calculated quantity
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Guidelines for UsingSignificant Figures
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Any digit that is not zero
is significant
Example: 845 cm has 3 SFs
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Zeros between nonzero digits
are significant
Example: 40,501 kg contains 5 SFs
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Zeros to the left of the first
nonzero digit are
not significant
Example: 0.008 L contains 1 SF
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If the number is >1, then all
the zeros written to the right
of the decimal point is
significant
Example: 2.00 mg has 3 SFs
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If a number is <1, the zeros
that are at the end of the
number and the zeros that are
between nonzero digits are
significant
Examples: 0.090 kg has 2 SFs
0.0405 g has 3 SFs
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For numbers that do not contain
decimal points, the trailing zeros
(that is, zeros after the last
nonzero digit) may or may not
be significant
Example: 400 can be expressed as
4 x 102 for 1 SF
4.0 x 102 for 2 SFs
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Rounding Off
A number is rounded off to the
desired number of significant
figures by dropping one or more
digits to the right
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Rounding Off Rules
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When the first digit dropped
is <5, the last digit retained
should remain unchanged
Example: 4.13 can be rounded off to 4.1
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0011 0010 1010 1101 0001 0100 1011When it is >5, 1 is added to the
last digit retained
Example:
4.17 can be rounded off to 4.2
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When it is exactly 5, 1 is added
to the last digit retained if
that digit is odd,
but remains as is when
it is even
Examples: 4.15 can be rounded off to 4.2
4.45 can be rounded off to 4.4
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In chain calculations, only
the final answer is rounded
off to the correct number of
significant figures
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Addition and Subtraction
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In addition and subtraction,
the answer cannot have more
digits to the right of the
decimal point than either of the
original numbers
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Example 89.332
+ 1.1
90.432
one digit after the decimal pt.
round off to 90.4
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Multiplicationand Division
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In multiplication and division,
the number of significant figures
in the final product or quotient is
determined by the original
number that has the smallest
number of significant figures
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Examples:
2.8 x 4.5039 =
12.61092 round off to 13
6.85/112.04 =
0.0611388789 round off to 0.0611
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Scientific Notation
used when working with very large and
very small numbers
expressed in the form:
N x 10n
where N- number between 1 and 10
n- exponent, + or - integer
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If the decimal point
has to be moved:
to the left n is +
to the right n is -
Examples:
568.762 = 5.68762 x 102 n = 2
0.00000772 = 7.72 x 10-6 n = - 6
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Addition and Subtraction
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• To add or subtract using scientific notation, write each quantity, say N1 and N2 -with the same exponent n then combine N1 and N2 the exponents remain the same
Example:
(7.4 x 103) + (2.1 x 103) = 9.5 x 103
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Multiplicationand Division
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• To multiply numbers expressed in scientific notation, we multiply N1 and N2 and then add the exponents together
Example:
(8.0 x 104) x (5.0 x 102)
= (8.0 x 5.0)( 104+2) = 40 x 106
= 4.0 x 107
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To divide using scientific
notation, we divide
N1 and N2 and then subtract
the exponents
Example:
(6.9 x 107)/(3.0 x 10-5) = (6.9/3.0) x 107-(-5)
= 2.3 x 1012
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Unit Conversions
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0011 0010 1010 1101 0001 0100 1011SI Base Units
Base Quantity Name of Unit Symbol
Length meter m
Mass kilogram kg
Time second s
Electrical current ampere A
Temperature kelvin K
Amount of substance mole mol
Luminous intensity candela cd
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Prefixes used with SI Units
Prefix Symbol Meaning Example
Tera- T 1012 1 terameter (Tm) = 1 x 1012 m
Giga- G 109 1 gigameter (Gm) = 1 x 109 m
Mega- M 106 1 megameter (Mm) = 1 x 106 m
Kilo- k 103 1 kilometer (km) = 1 x 103 m
Deci- d 10-1 1 decimeter (dm) = 0.1 m
Centi- c 10-2 1 centimeter (cm) = 0.01 m
Milli- m 10-3 1 millimeter (mm) = 0.001 m
Micro- μ 10-6 1 micrometer (μm) = 1 x 10-6 m
Nano- n 10-9 1 nanometer (nm) = 1 x 10-9 m
Pico- p 10-12 1 picometer (pm) = 1 x 10-12 m
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Unit Conversion Factors
LENGTH
1 m = 100 cm = 1000 mm = 106 μm = 109 nm
1 km = 1000 m = 0.6214 mi
1 in = 2.540 cm
1 ft = 30.48 cm
1 yd = 91.44 cm
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TIME
1 min = 60 s
1 h = 3600 s
1 d = 86,400 s
1 y = 365.24 d = 3.156 x 107 s
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MASS
1 kg = 103 g = 2.205 lb
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VOLUME
1 liter= 1000 mL = 1000 cm3 = 1 dm3 = 10-3 m3
1 ft3 = 0.02832 m3 = 28.32 liters = 7.477 gallons
1 gallon = 3.788 liters
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Simple Conversion
Convert 22 inches into feet
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Answer
• 22 in x (1 ft/12 in) = 1.8 ft
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Multiple Conversion
Convert 2,700 mL into gallon
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Answer
2700 mL x (1 L/1000 mL) x (1 gal/3.788 L)
= 0.7128 gal
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Determine the number of SFs of the following measurements
1. 478 cm 6. 0.043 kg2. 6.01 g 7. 560 mg3. 0.825 m 8. 453.2 cm4. 3001 km 9. 2.60 dm5. 1,020 mL 10. 200 L
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Perform the operations and express the answers to the correct number of SFs
1. 11,254.1 g + 0.1983 g 2. 0.0154 kg / 88.3 mL3. 66.59 L – 3.113 L 4. 2.64 x 103 cm + 3.27 x 102 cm5. 8.16 m x 5.1355 m
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Express the ff. numbers in scientific notation1. 0.000000027
2. 0.096
3. 356
4. 602,200,000,000,000,000,000,000
5. 0.00000000000000000000000166
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1.A person’s average daily intake of glucose (a form of sugar) is 0.0833 pound (lb). What is this mass in milligrams?
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2.An average adult has 5.2 L of blood. What is the volume of blood in m3?