1 Units and significant figures
1.1 SI units
Base quantity Name Symbol
length meter m
mass kilogram kg
time second s
electrical current ampere A
temperature kelvin K
amount of x mole mol
luminous intensity candela cd
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1.2 Prefixes
Prefix Symbol Exponent
giga G 109
mega M 106
103
ul
kila k
hecta h 102
deca da 101
deci d 10−1
centi c 10−2
Po
mili m 10−3
micro µ 10−6
nano n 10−9
pico p 10−12
1.3 Significant figures
a
• all non-zero digits are significant
• zeros between two significant figures are significant
nn
• zeros at the beginning of a number are never significant
• zeros at the end of a number are significant is a decimal point is written in the numbers
• examples:
– 321.5 → (4)
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– 4.006 → (4)
– 00 125.45 → (3)
– 125.350 → (6)
– 12535 0 → (5)
• multiplication and division
– answer has the same amount of significant digits of the number of significant figures of the number
with the fewest significant figures
– 10.34 · 9.12 = 94.3 00
• addition and subtraction
– same amount of significant figures as there are significant figures in the number with the least amount
of significant figures
– 10, 34 + 9. 125 = 19.46 5
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2 Precision and accuracy
2.1 Definitions
• prescision: how close the measurements are to one another (reproducibility)
• accuracy: how close a measurement is to the actual value
• systematic error: values that are either all higher or all lower than the actual values (offset in measurement
apparatus)
• random area: in the absence of systematic errors, values that are higher and lower than the actual value
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2.2 Diagrams
ul
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a
nn
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2
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3 Conversion factors
Quantity Equivalent values
Mass 1kg = 1000g = 0.001 metric ton = 2.20462lbm = 35.27392 oz
1lbm = 16oz = 453.593g = 0.453593kg
Length 1m = 100cm = 1000mm = 0.001km = 39.37 inches = 3.2808ft = 1.0936yd
1ft = 12 inches = 0.3048m = 304.8mm
Volume 1m3 = 1000 l = 106 cm3 = 35.3145ft3 = 220.83 imp gall = 264.12 US gall
1 ft3 = 1728 inches3 = 28.317 l = 0.028317m3
Force 1N = 1kg m/s2 = 105 dynes = 0.22481 lbf
Pressure 1atm = 1.01325 x 10 N/m (Pa) = 101.325kPa = 1.01325 bar = 760mmHg by 0◦ (torr) = 14.696psi
5 2
Power 1J = 1Nm = 107 erg = 2.778 x 10−7 kW h = 0.23901cal = 0.7376ft lbf = 9.486 x 10−4 Btu
r
Temperature T(◦ F) = 1.8 ◦ C + 32
T(◦ C) = (5/9)(◦ F - 32)
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T(K) = ◦ C + 273.15
T(◦ R) = ◦ F + 459.6
ul
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nn
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3
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4 Unit conversions
4.1 Unit conversions
• If one strand of optic fibre weighs 1.19x10−3 lbm /m, what is the mass (in kilograms) of a cable made of
six strands of optical fibre, each one long enough to link New York and Paris (8.84x103 km)?
1.19x103 lbm 1000m 4.54x10−1 kg 8.84x103 km 6
1m 1km 1lbm 1 1
(1.19x10−3 )(103 )(4.54x10−1 kg)(8.84x103 )(6)
= 2.87x104 kg
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4.2 Temperature unit conversions
• Celcius scale
ul
– based on the phase change of water
• Kelvin(absolute) scale
– same size degree unit as the Celcius scale
Po
– different zero points
– 0K = absolute zero
• Farenheit scale
– different size degree unit than Celcius and Kelvin scales
– different zero point
• Rankine (absolute) scale
a
– same size degree unit as Farenheit scale
nn
– different zero points
– 0◦ R = absolute zero
Celcius Kelvin Farenheit Rankine
Absolute zero -273.15 0 -459.67 0
Freezing point of water 0 271.15 32 491.67
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Boiling point of water 100 373.15 212 671.64
• Equivalent temperature changes
– 1.8∆◦ F = ∆◦ C
– 1.8∆◦ R = ∆K
– ∆◦ F = ∆◦ R
– ∆◦ C = ∆K
• Temperature intervals
– 1.8◦ F in ◦ C
– 1.8◦ R in 1K
– 1◦ R in 1◦R
– 1◦ C in 1K
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