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AQA ALevel Physics Topic 1  Measurements and Their Errors; made directly in accordance with the AQA 7408 specification
SI units
mass (m) 
kilograms (kg) 
length (l) 
metres (m) 
time (t) 
seconds (s) 
amount of substance (n) 
moles (mol) 
temperature (t) 
kelvin (K) 
electric current (I) 
amperes (A) 
Derivation of SI Units
A derived unit is comprised of a combination of SI units. 
These can be derived by using the definition of the unit, or their equations eg. F=ma 
eg. to find the SI units of force (F), multiply the units of mass and acceleration to give kgms^2 (or N) 
This means that every unit can be broken down into its SI base units. 
Prefixes
Tera (T) 
10^12 
Giga (G) 
10^9 
Mega (M) 
10^6 
Kilo (K) 
10^3 
Centi (c) 
10^2 
Milli (m) 
10^3 
Micro (µ) 
10^6 
Nano (n) 
10^9 
Pico (p) 
10^12 
Femto (f) 
10^15 
These prefixes could be added before any SI units
Conversions between units
It is possible to convert between different units of the same quantity. Here are some examples listed below: 
1 eV = 1.6 × 10^–19 J 
1 kW h = 3 600 000 J or 3.6 MJ (×10^6) 
Types of Errors
Random error 
Cause variations in both directions and are usually uncontrollable 
Systematic error 
Caused by faults in the experimental method or apparatus 
Zero error 
A type of systematic error caused by uncalibrated equipment 
Parallax error 
A type of systematic error caused by the apparent position of an object due to the viewing angle 


Reviewing measurements
Precise 
Consistent and fluctuate around a mean value 
Accuracy 
A measurement that is close to the true value 
Repeatability 
The original person can redo the experiement and get the same results 
Reproducibility 
A different person does an experiment differently and gets the same results 
Resolution 
The smallest change in the quantity being measured that gives a recognisable change in reading 
Uncertainty
The bounds in which the accurate value can be expected to lie 
They should be given to the same number of significant figures as the data. 
Types of Uncertainity
Absolute 
Uncertainty given as a fixed quantity 
Fractional 
Uncertainty as a fraction of the measurement 
Percentage 
Uncertainty as a percentage of the measurement 
Resolution and Uncertainity
Readings are when one value is found 
Measurements are when the difference between 2 readings is found 
The uncertainty in a reading is +/ half the smallest division 
The uncertainty in a measurement is at least +/ 1 smallest division 
The resolution of an instrument will affect its uncertainty 
Digital readings and given values will either have the uncertainty quoted, or assumed to be +/ the last significant digit 
For repeated data, the uncertainty is half the range 
Reducing Uncertainity
You can reduce uncertainty in the following ways: 
• fixing one end of a ruler so there is only uncertainty in on reading 
• measuring multiple times 
• (for fractional and percentage) measure larger quantities 


Combining Uncertainties
Adding/subtracting data  ADD ABSOLUTE UNCERTAINTIES 
Multiplying/diving data  ADD PERCENTAGE UNCERTAINTIES 
Raising to a power  MULTIPLY PERCENTAGE UNCERTAINITY BY POWER 
Uncertainties in graphs
Uncertainties are shown as error bars on graphs 
A line fo best fit on a graph should go through all error bars (excluding anomalies) 
The uncertainity in a gradient can be found by lines of best and worst fit 
This can be done using the gradients of the steepest and shallowest lines of best fits 
You can also use these two lines to find the uncertainty in the yintercept 
Estimation of physical quantities
Orders of magnitude are powers of ten which describe the size of an object 
These can be used to compare the sizes of objects 
Estimation is a skill used to approximate the values of physical quantities, in order to make comparisons, or to check if a value calculated is reasonable. 
Variables
Dependant 
The variable that is being measured 
Independent 
The variable that is being changed 
Control 
Other variables that stay the same 

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