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Skill 5 of 14
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# Fundamental units

There do exist

• other position units than the metre, for example miles, inches, yards and feet,
• other time units than the second, for example minutes, days and centuries and thus also
• other speed units than the metre-per-second, for example miles-per-hour.

It might be smart to pick one unit for each property as a “standard” unit. People may use other units if they want, but at least we will all have some common ground. Let’s choose some default units for the fundamental properties and call them fundamental units:

Fundamental units
PositionMetre$\mathrm m$
TimeSecond$\mathrm s$
Quantity$-$$-$
MassGramme$\mathrm g$
TemperatureKelvin$\mathrm K$
ChargeCoulomb$\mathrm C$
LuminosityCandela$\mathrm{cd}$

We did not give ‘quantity’ a unit as it is just a unit-less count (see the Existence discipline).

Prefixes don’t matter; kilometres and nanoseconds just mean ‘1000 metres’ and ‘a billionth second’. They are still fundamental units, just multiplied a couple of times with prefixes. So,

• $\mathrm m$ and $\mathrm s$ are fundamental units for position and time,
• $\mathrm{km}$ and $\mathrm{\mu s}$ (microsecond) are as well, just with prefixes, whereas
• $\mathrm{mile}$ and $\mathrm{hr}$ (hour) are not fundamental units (they are not just the metre or second with a prefix).

Combined (derived) properties naturally have combined (derived) fundamental units, such as metres-per-second $\mathrm{m/s}$ and cubic metres $\mathrm{m^3}$.

• $\mathrm{m/s}$ and $\mathrm{m^3}$ are fundamental units for velocity and volume,
• $\mathrm{km/s}$ and $\mathrm{mm^3}$ (cubic millimetre) are as well, just with prefixes, whereas
• $\mathrm{km/hr}$ and $\mathrm{L}$ (litre) are not fundamental units.

Note that all this was just a choice from our side. We could just as well have chosen the ‘hour’ as the fundamental time unit instead of the ‘second’. It wouldn’t matter, we just had to choose something. Our choice of units here matches the units in the official, international so-called SI1 unit system.2 See an overview and more description of the SI system in Resource: The SI unit system.

In everyday life other units are often used (highly depending on country and culture). We buy milk in litres or gallons, use minutes and hours, dress according to degree Celsius or Fahrenheit etc. In professional and educational contexts, we see units invented for convenience such as nautical miles on the seas, pinches and teaspoons in the bakery and lightyears in space.

An overview of several often-used non-SI units can be found in Resource: Often-used units.

References:

1. The International System of Units (SI)’ (book), B. Inglis, J. Ullrich and others, Bureau International des Poids et Mesures (BIPM), 9th ed., 2019, www.bipm.org/utils/common/pdf/si-brochure/SI-Brochure-9.pdf, chapter 3
2. Guide for the Use of the International System of Units (SI)’ (article), Ambler Thompson & Barry N. Taylor, National Institute of Standards and Technology, 2008, physics.nist.gov/cuu/pdf/sp811.pdf