3.1 Measurements and Their Errors
3.1.1 Use of SI Units & Their Prefixes:
Base Units:
Quantity Unit What it measures
Metre m Length
Kilograms kg Mass
Second s Time
Ampere A Electrical current
Kelvin K Temperature
Mole mol Amount of substance
Derived units come from these base units, e.g.:
s-1 = Frequency
Force = Mass (kg) x acceleration (ms-2) ∴ The derived units for force = kgms-2 (waves and other
Energy = ½ mv2 (we ignore constants like ½). Energy = kg x (ms -1)2 = kgm2s-2 things)
Prefixes:
Adding Prefixes:
Name Prefix Power of ten
Do OPPOSITE:
Tera T x1012
Giga G x109 5J --> kJ (k = x103)
Mega M x106 = 5 x 10-3 = 0.005kJ
Kilo k x103 Getting Rid of Prefixes:
Centi c x10-2 Do NORMAL:
Milli m x10-3 67,000cm --> m (c = x10-2)
Micro μ x10-6 = 67,000 x 10-2 = 670m
Nano n x10-9 Powers
Pico p x10-12 67,000cm3 --> m3
Femto f x10-15 = 67,000 x (10-2)3 = 0.067m3
3.1.2 Limitation of Physical Measurements:
Random Error: The readings are scattered about the true value:
Caused by continuous & unpredictable fluctuations in physical quantities.
Can be reduced by taking more readings and finding an average, or by drawing a graph and
finding a line of best fit.
Found on a graph by a scatter in the results (above & below the line of best fit).
Possible causes: varying temperature, kinks in a wire, reaction time, different resistances,
balls having different bouncinesses, not stirring water & the heat distributing over time
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3.1.1 Use of SI Units & Their Prefixes:
Base Units:
Quantity Unit What it measures
Metre m Length
Kilograms kg Mass
Second s Time
Ampere A Electrical current
Kelvin K Temperature
Mole mol Amount of substance
Derived units come from these base units, e.g.:
s-1 = Frequency
Force = Mass (kg) x acceleration (ms-2) ∴ The derived units for force = kgms-2 (waves and other
Energy = ½ mv2 (we ignore constants like ½). Energy = kg x (ms -1)2 = kgm2s-2 things)
Prefixes:
Adding Prefixes:
Name Prefix Power of ten
Do OPPOSITE:
Tera T x1012
Giga G x109 5J --> kJ (k = x103)
Mega M x106 = 5 x 10-3 = 0.005kJ
Kilo k x103 Getting Rid of Prefixes:
Centi c x10-2 Do NORMAL:
Milli m x10-3 67,000cm --> m (c = x10-2)
Micro μ x10-6 = 67,000 x 10-2 = 670m
Nano n x10-9 Powers
Pico p x10-12 67,000cm3 --> m3
Femto f x10-15 = 67,000 x (10-2)3 = 0.067m3
3.1.2 Limitation of Physical Measurements:
Random Error: The readings are scattered about the true value:
Caused by continuous & unpredictable fluctuations in physical quantities.
Can be reduced by taking more readings and finding an average, or by drawing a graph and
finding a line of best fit.
Found on a graph by a scatter in the results (above & below the line of best fit).
Possible causes: varying temperature, kinks in a wire, reaction time, different resistances,
balls having different bouncinesses, not stirring water & the heat distributing over time
1
