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SI units and prefixes

Every quantity in physics carries a unit, and every unit is built from the same six blocks. Learn the blocks, the ten prefixes that scale them, and the habit of carrying units through a calculation rather than sticking them on at the end.

Year 12AQA 3.1.1

IN THIS TOPIC

  • Name the six SI base quantities used at A-level and their units.
  • Recognise derived units as combinations of base units, and unpack one when asked.
  • Use the ten SI prefixes with standard form, and convert between units of the same quantity, such as J and eV, or J and kW h.

WHAT YOU PROBABLY THINK

Units are labels you attach once the number is finished.

Six units underneath everything

The SI system rests on a small set of base units. A-level physics uses six of them: the kilogram for mass, the metre for length, the second for time, the ampere for electric current, the kelvin for temperature and the mole for amount of substance. There is a seventh, the candela for light intensity, which the specification excludes, and you are not expected to recall formal definitions of any of them.

The six SI base quantities and their unitsmasskglengthmtimescurrentAtemperatureKamountmol
FIG. 1The six base quantities and their units. Every other unit in the subject is assembled from these.

Derived units

Everything else is a derived unit: a combination of base units produced by an equation. Because F = ma, force is measured in kg m s−2, a combination used so often it gets its own name, the newton. The pascal is a newton spread over a square metre, and the joule is a newton pushed through a metre. A named unit is shorthand, never new information.

A derived unit assembled from base units: the newtonkgms⁻²N1 N = 1 kg m s⁻²
FIG. 2One newton is one kilogram metre per second squared. The name is an abbreviation for the base-unit combination, not a separate thing.

This is why units deserve better than an afterthought. If you keep them attached during a calculation, the answer arrives wearing the right unit automatically, and an answer wearing the wrong one is an early warning that the working has gone astray.

Prefixes and standard form

Real quantities span an enormous range, so the SI attaches prefixes that multiply a unit by a power of ten. AQA requires exactly ten of them:

PrefixSymbolMultiplier
teraT1012
gigaG109
megaM106
kilok103
centic10−2
millim10−3
microμ10−6
nanon10−9
picop10−12
femtof10−15
The SI prefixes from femto to tera on a powers-of-ten linef10⁻¹⁵p10⁻¹²n10⁻⁹µ10⁻⁶m10⁻³110⁰k10³M10⁶G10⁹T10¹²
FIG. 3The ten prefixes on a power-of-ten line. Nine of them step in threes; centi is the odd one out at ten to the minus two.

Nine of the ten sit at multiples of three, which makes them easy to place. The exception is centi at 10−2, kept alive by the centimetre. In working, convert prefixed values to standard form in the base unit first: 250 μm becomes 2.5 × 10−4 m, and from there the calculation cannot trip over the prefix.

Converting between units of the same quantity

Some quantities are measured in more than one unit, and the specification names two conversions. Energy in electronvolts: one eV is the energy an electron gains crossing one volt, 1 eV = 1.60 × 10−19 J, so multiply by that factor to reach joules. Energy in kilowatt hours: one kW h is a kilowatt delivered for an hour, 1 kW h = 3.6 × 106 J, because 1000 W runs for 3600 s.

The pattern is the same both times. Write the conversion factor as an equality, decide which way you are travelling, and multiply. Guessing whether to multiply or divide is where these marks are lost.

THE EXAM BIT

  • The ten prefixes are not printed in the data booklet. Learn all ten, including the awkward centi at 10−2.
  • Squared units square the prefix: 1 cm2 is 10−4 m2, not 10−2. Convert the length first, then square.
  • Use your calculator's power key for standard form and keep numbers in it throughout; retyping rounded intermediates is how the last significant figure goes wrong.
  • Going from eV to J, multiply by 1.60 × 10−19. A photon energy that comes out at 1019 J means the conversion went the wrong way.
  • Write the unit on the answer line every time. A correct number with a missing or wrong unit routinely drops the final mark.

CHECK YOURSELF

(a) Write 250 μm in metres, in standard form. (b) An electron has 5.0 keV of kinetic energy. How many joules is that?

Show a hint

Take one prefix at a time: micro first, then kilo, then the eV to J factor.

Show the answer

(a) Micro means 10−6, so 250 μm = 250 × 10−6 m = 2.5 × 10−4 m.

(b) 5.0 keV = 5.0 × 103 eV. Each eV is 1.60 × 10−19 J, so the energy is 5.0 × 103 × 1.60 × 10−19 = 8.0 × 10−16 J.

Ten prefixes. Learn them all.

The data sheet does not print them.

No animated video for this topic yet; these notes stand alone. InkPhysics on YouTube.