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PHYSICS
QUANTITIES AND UNITS
Key Word : Base Quantities, Derived Quantities, Scientific notation,
Significant digit, Dimension, SI
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CONCEPT MAP
QUANTITIES AND UNITS
QUANTITIES UNITS DIMENSION MEASUREMENT SIGNIFICANT DIGITS
BASEQUANTITIES
DERIVEDQUANTITIES LENGTH MASS TIME
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objective
• To analysis quantities and units in physics.
• To differ between base quantities andderived quantities.
• To determine SI from base quantities andderived quantities.
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Quantities is something that can bemeasured and written by digit
Units is something that show howmuch the result of measurement.
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Base Quantities.
The unit in which these
quantities are
measured
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Derived quantities is
combination from more than
one quantities
Example :Velocity, acceleration, volume, force,density, work
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PrefixesPrefixes are used tochange SI units by
power of 10
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Prefixes Used with SI units
Prefix Symb
ol Multiplier Scientific
Notation
Example
femto f 1/1 000 000 000 000 000 10-15 Femtosecond (fs)
pico p 1/1 000 000 000 000 10-12 picometer (pm)
nano n 1/1 000 000 000 10-9 nanometer (nm)
micro 1/1 000 000 10-6 microgram (g)
milli m 1/1 000 10-3 milligram (mg)
centi c 1/100 10-2 centimeter (cm)
deci d 1/10
10
-1
deciliter (dL) kilo k 1000 103 Kilometer (km)
mega M 1 000 000 106 megagram (Mg)
giga G 1 000 000 000 109 Gigameter (Gm)
tera T 1 000 000 000 000 1012
Terameter (Tm)
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SI Base Quantities
Base Quantities Base Unit Symbol
Length meter m
Mass kilogram kg Time second s
Temperature Kelvin K
Amount of Substance mole mol Electric Current ampere A
Luminous Intensity candela cd
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Derived units are
combinations of the base unit
Example :
m/s, used to measure speed
The joule, kg m2 /s2, used to measure energy
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Objectives
To define the SI standards of measurement
• To use common metric prefixes.
•
To distinguish between accuracy andprescision
• To indicate the precision of measuredquantities with significant digit
• To perform arytmatic operations withsignifican digits
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Measurement is
a comparison between an
unknown quantities and aStandard
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Scientific Notation express decimal places as power of
10
M x 10n
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Significant Digits
The valid digits in a measurement arecalled the significant digits.
The rules how to determine the number ofsignificant digits: – Nonzero digits are always significant. – All final zeros after the decimal point are significant – Zeros used solely as placeholders are not significant
The number of significant digits in measurementis an indication of the precision with which themeasurement was taken.
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Precision
Precision describes the degree of
exactness of a measurement.
Precision depends on the
instrument used to make the
measurement
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Accuracy
Accuracy describes how well theresults of an experiment agreewith the standard value.
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Expressing quantiites
in scientific notation
5800 m
5800 m = 5.8 x 10
3
m
0.000 508 kg
0.000 508 kg = 5.08 10
-4
kg
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Addition and subtraction using Scientific
Notation
4 x 108 m + 3 x 108 m
Strategy : If the numbers have the same
exponent, n , add or subtract the values of Mand keep the same n
4 x 108 m + 3 x 108 m = (4+3) x 108 m
= 7 x 108 m
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4.1 x 10-6 kg - 3.0 x 10-7 kg
Strategy : If the exponent are not the same, movethe decimal to the left or right until they are thesame. Then add or subtract M
4.1 x 10-6 kg - 3.0 x 10-7 kg= 4.1 x 10-6 kg – 0.30 x 10-6 kg
= (4.1 – 0.30) x 10-6 kg
= 3.8 x 10-6 kg
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4.02 x 106 m + 1.89 x 102 m
Strategy : if the magnitude of one number isquite small when compared to the othernumber, its effect on larger number issignificant. The smaller number can be treatedas zero.
4.02 x 106 m + 1.89 x 102 m = 40 200 x 102 m + 1.89 x 102 m
= (40 200 + 1.89) x 102 m
= 40 201.89 x 102 m
= 4.02 x 106 m
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Multipication and Division Using Scientific Notation
(4x 103 kg)(5 x 1011 m)
Strategy : multiply the values of M and add the
exponents, n. Muliply the unit
(4x 103 kg)(5 x 1011 m) = (4 x 5) x 103+11 kg.m= 20 x 1014 kg.m
= 2 x 1015 kg.m
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Strategy : divide the values of M and substract the
exponent of the divisor from the exponent of th
dividend.
23
36
102
108
m
m
mm
m
m 923)3(6
23
36
104102
8
102
108
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Determine significant
digits
186 km has three significant digits
186 000 m has six significantdigits
1.86 x 105 m has three significant
digits1.86000 x 105 m has six significantdigits
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Significant digits in additon and substraction
Add 24.686 m + 2.343 m + 3.21 m
Strategy : Note that 3.21 m has the least number of decimalplaces. Round off the result to the nearest hundredth of meter.
Calculations:
24.686 m
2.343 m
+ 3.21 m30.239 m
The correct answer is 30.24 m
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Significant digits in multiplication and division
Multiply 3.22 cm by 2.1 cm.
Strategy : The factor 2.1 cm, contains two
significant digits. State the product in twosignificant digits.
Calculations:
3.22 m
x 2.1 m6.762 m
The correct answer is 6.8 cm2
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Divide 36.5 m by 3.414 s Strategy :The less precise factor contains three
significant digits. State the answer in threesignificant digits.
Calculations:
The correct answer is 10.7 m/s
sm
s
m
/ 691.10414.3
5.36