A measurement is a number and a unit. The SI system defines seven base units, and every other unit in physics is derived from them. Prefixes scale a unit by powers of ten.
To measure a quantity is to compare it with a fixed reference amount of the same kind. That reference amount is the unit. The result of the comparison is a number: how many units the quantity contains.
“The rod is 5 m long” means the rod is 5 times as long as one metre. “5 long” says nothing, because 5 m, 5 cm and 5 km are different lengths.
If the unit changes, the number changes to match, and the quantity stays the same. 5 m = 500 cm.
Physics does not need an independent standard for every quantity. A small set of base quantities is chosen, each with a base unit. The unit of every other quantity is a combination of base units, called a derived unit.
Speed is distance divided by time. So its unit is the metre divided by the second, m/s. Force is mass times acceleration, so its unit is kg m/s², given the name newton (N).
The unit of area is the square metre and the unit of volume is the cubic metre. Are these base units or derived units?
Both are derived. Area is length × length, so its unit is m × m = m². Volume is length × length × length, so its unit is m³.
Neither needs its own standard. Each is defined from the metre.
The International System of Units, called SI from its French name, is used in science worldwide. It has seven base quantities and seven base units.
The seven SI base units. Mechanics uses the metre, kilogram and second. The ampere, kelvin, mole and candela are needed for electricity, heat, chemistry and light.
Since 2019, each base unit has been defined by fixing the exact value of a constant of nature. For example, the second is defined from the frequency of a particular radiation of the caesium-133 atom, and the metre from the speed of light, exactly 299,792,458 m/s. Any laboratory with the right equipment can reproduce the units, without comparing against a single physical object.
A length measured in Mumbai must mean the same when it is read in Tokyo. That requires the same units, defined the same way, in both places.
Mixing systems causes real failures. In 1999 NASA lost the Mars Climate Orbiter. One team’s software reported thruster impulse in pound-force seconds; the navigation software expected newton-seconds. The spacecraft’s path was wrong by a factor of about 4.45, and it entered the Martian atmosphere far too low.
Lengths in physics range from about 10⁻¹⁵ m (the size of a proton) to about 10²⁶ m (the observable universe). Instead of new units for each scale, SI uses prefixes. Each prefix multiplies the unit by a fixed power of ten.
kilo (k) = 10³, so 1 km = 1000 m. milli (m) = 10⁻³, so 1 mm = 0.001 m. micro (µ) = 10⁻⁶. nano (n) = 10⁻⁹. The unit is unchanged; the prefix changes the power of ten.
A nanometre is 10⁻⁹ m. How many nanometres are in one metre, and where are nanometres a convenient unit?
1 m = 10⁹ nm, one thousand million nanometres.
The distance between neighbouring atoms in a solid is about 0.1 to 0.5 nm. The wavelength of visible light is about 400 to 700 nm. In metres, these would be written 0.0000000004 m or 5 × 10⁻⁷ m. In nanometres they are small, readable numbers.
1A complete measurement consists of…
2A derived unit is one that…
3Is each unit a base unit or a derived unit?
4The International System of Units is known by the abbreviation ____.
5Which three base units does mechanics use?
6What does the prefix “kilo” do to a unit?
Next: how many digits of a measurement carry real information.
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