Measurements and their errors Flashcards
Random error
Measurements vary due to unpredictable circumstances. They can’t be corrected and can only be mitigated by making more measurements and calculating a new mean.
Systematic error
Measurements differ from the true value by a consistent amount each time. They can be corrected by using a different technique to take measurements.
Precision
How close measurements are to each other and the mean.
Accuracy
How close a measurement is to the true value.
Repeatable
When the original experimenter repeats the investigation using the same method and equipment and obtains the same results.
Reproducible
When somebody else repeats the investigation or the investigation is performed using different equipment or techniques and the same results are obtained.
Resolution
The smallest change in a quantity being measured that gives a perceptible change in the reading.
Readings
Require a single judgement.
Measurements
Require two judgements.
Uncertainty for a reading
+- half the smallest scale division.
Uncertainty for a measurement
+- the smallest scale division.
Base quantities and their units
Length (metre/m), Mass (kilogram/kg), Time (second/s), Electric current (ampere/A), Temperature (kelvin/K), Amount of substance (mole/mol), Luminous intensity (candela/cd).
Joule in terms of base units
kg m^2 s^-2
Volt in terms of base units
kg m^2 s^-3 A^-1
Newton in terms of base units
kg m s^-2
T, tera
10^12
G, giga
10^9
M, mega
10^6
k, kilo
10^3
c, centi
10^-2
m, mili
10^-3
μ, micro
10^-6
n, nano
10^-9
p, pico
10^-12
f, femto
10^-15
Number of significant figures for a calculated quantity
Equal to the least number of significant figures used in the calculation.
Number of decimal places of the logarithm value
Equal to the number of significant figures of the value.
Percentage uncertainty
The absolute uncertainty divided by the measured value multiplied by one hundred.
When adding or subtracting data with uncertanties
Add the absolute uncertanties.
When multiplying or dividing data with uncertanties
Add the percentage uncertanties.
When raising data with an uncertainty to a power
Multiply the percentage uncertainty by that power.
When multiplying data with an uncertainty by a constant
Multiply the absolute uncertainty by that constant but not the percentage uncertainty.
Percentage uncertainty from a graph
|best gradient - worst gradient|/best gradient x 100% or |best y intercept - worst y intercept|/best y intercept x 100%
Order of magnitude for the radius of a proton
10^-15 m
Order of magnitude for the radius of an atom
10^-10 m
Order of magnitude for the radius of the earth
10^7 m
If percentage uncertainty < 1%
Give to 1 sig fig
