physics (significant figures)
TRANSCRIPT
42510011 0010 1010 1101 0001 0100 1011
THE NUMERICAL SIDE OF PHYSICS
4251
0011 0010 1010 1101 0001 0100 1011
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
4251
0011 0010 1010 1101 0001 0100 1011
Significant Figures
• the number of meaningful digits in a measured or calculated quantity
42510011 0010 1010 1101 0001 0100 1011
Guidelines for UsingSignificant Figures
4251
0011 0010 1010 1101 0001 0100 1011
Any digit that is not zero
is significant
Example: 845 cm has 3 SFs
4251
0011 0010 1010 1101 0001 0100 1011
Zeros between nonzero digits
are significant
Example: 40,501 kg contains 5 SFs
4251
0011 0010 1010 1101 0001 0100 1011
Zeros to the left of the first
nonzero digit are
not significant
Example: 0.008 L contains 1 SF
4251
0011 0010 1010 1101 0001 0100 1011
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
4251
0011 0010 1010 1101 0001 0100 1011
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
4251
0011 0010 1010 1101 0001 0100 1011
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
4251
0011 0010 1010 1101 0001 0100 1011
Rounding Off
A number is rounded off to the
desired number of significant
figures by dropping one or more
digits to the right
42510011 0010 1010 1101 0001 0100 1011
Rounding Off Rules
4251
0011 0010 1010 1101 0001 0100 1011
When the first digit dropped
is <5, the last digit retained
should remain unchanged
Example: 4.13 can be rounded off to 4.1
4251
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
4251
0011 0010 1010 1101 0001 0100 1011
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
4251
0011 0010 1010 1101 0001 0100 1011
In chain calculations, only
the final answer is rounded
off to the correct number of
significant figures
42510011 0010 1010 1101 0001 0100 1011
Addition and Subtraction
4251
0011 0010 1010 1101 0001 0100 1011
In addition and subtraction,
the answer cannot have more
digits to the right of the
decimal point than either of the
original numbers
4251
0011 0010 1010 1101 0001 0100 1011
Example 89.332
+ 1.1
90.432
one digit after the decimal pt.
round off to 90.4
42510011 0010 1010 1101 0001 0100 1011
Multiplicationand Division
4251
0011 0010 1010 1101 0001 0100 1011
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
4251
0011 0010 1010 1101 0001 0100 1011
Examples:
2.8 x 4.5039 =
12.61092 round off to 13
6.85/112.04 =
0.0611388789 round off to 0.0611
4251
0011 0010 1010 1101 0001 0100 1011
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
4251
0011 0010 1010 1101 0001 0100 1011
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
42510011 0010 1010 1101 0001 0100 1011
Addition and Subtraction
4251
0011 0010 1010 1101 0001 0100 1011
• 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
42510011 0010 1010 1101 0001 0100 1011
Multiplicationand Division
4251
0011 0010 1010 1101 0001 0100 1011
• 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
4251
0011 0010 1010 1101 0001 0100 1011
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
42510011 0010 1010 1101 0001 0100 1011
Unit Conversions
4251
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
4251
0011 0010 1010 1101 0001 0100 1011
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
4251
0011 0010 1010 1101 0001 0100 1011
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
4251
0011 0010 1010 1101 0001 0100 1011
TIME
1 min = 60 s
1 h = 3600 s
1 d = 86,400 s
1 y = 365.24 d = 3.156 x 107 s
4251
0011 0010 1010 1101 0001 0100 1011
MASS
1 kg = 103 g = 2.205 lb
4251
0011 0010 1010 1101 0001 0100 1011
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
4251
0011 0010 1010 1101 0001 0100 1011
Simple Conversion
Convert 22 inches into feet
4251
0011 0010 1010 1101 0001 0100 1011
Answer
• 22 in x (1 ft/12 in) = 1.8 ft
4251
0011 0010 1010 1101 0001 0100 1011
Multiple Conversion
Convert 2,700 mL into gallon
4251
0011 0010 1010 1101 0001 0100 1011
Answer
2700 mL x (1 L/1000 mL) x (1 gal/3.788 L)
= 0.7128 gal
4251
0011 0010 1010 1101 0001 0100 1011
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
4251
0011 0010 1010 1101 0001 0100 1011
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
4251
0011 0010 1010 1101 0001 0100 1011
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
4251
0011 0010 1010 1101 0001 0100 1011
1.A person’s average daily intake of glucose (a form of sugar) is 0.0833 pound (lb). What is this mass in milligrams?
4251
0011 0010 1010 1101 0001 0100 1011
2.An average adult has 5.2 L of blood. What is the volume of blood in m3?