Smallest magnitude of distance

10^{-15} m (sub-nuclear particles)

Largest magnitude of distance

10^{25} m (extent of the visible universe)

Smallest magnitude of mass

10^{-30} kg (electron)

Largest magnitude of mass

10^{50} kg (mass of the universe)

Smallest magnitude of time

10^{-23} s (passage of light across a nucleus)

Largest magnitude of time

10^{18} s (age of the universe)

SI unit for mass

kilograms, kg

SI unit for distance

metres, m

SI unit for time

seconds, s

SI unit for amount of substance

mole, mol.

SI unit for electric current

ampere, A

SI unit for temperature

kelvin, K

What unit is used when calculating the cost of heating?

kW h

1 J = ? eV

1 elementary charge

Define: random error

Errors in measurement that lead to measurable values being inconsistent when repeated measures of a constant attribute or quantity are taken.

Sources of random error (4)

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- unpredictable fluctuations in the readings of a measurement apparatus
- the experimenter's interpretation of the instrumental reading
- effects of a change in the surroundings
- readability of the instrument

Define: systematic error

An error that is not determined by chance but is introduced by an inaccuracy (as of observation or measurement) inherent in the system.

Sources of systematic error (2)

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- an instrument with zero error
- a wrongly calibrated instrument

Define: precision

A measurement of how close a number of measurements of the same quantity agree with each other. It is limited by random error.

Define: accuracy

How close the measurement is to the true value of the quantity being measured. It is reduced by systematic error.

How can random errors be reduced?

By repeated readings.

(N.B. systematic error cannot be reduced by repeat readings)

How can absolute uncertainty be calculated?

When marking the absolute uncertainty in a piece of data, we simply add ± 1 of the smallest significant figure.

How can fractional uncertainty be calculated?

To calculate the fractional uncertainty of a piece of data we simply divide the uncertainty by the value of the data.

How can percentage uncertainty be calculated?

To calculate the percentage uncertainty of a piece of data we simply multiply the fractional uncertainty by 100.

Determine the uncertainties in addition and subtraction.

When performing additions and subtractions we simply need to add together the absolute uncertainties.

Determine the uncertainties in multiplication and division

When performing multiplications and divisions we simply add together the percentage uncertainties.

Determine the uncertainties in powers.

Multiply the uncertainty by the power

Define: vector quantity

A quantity with magnitude and direction

Define: scalar quantity

A quantity with only magnitude