Units and MeasurementIntroduction
The sports teacher asks Riya and Aman to check the new cricket pitch on the school ground. Aman crawls along it counting hand spans and gets about 100. Riya walks it and counts 27 paces. The groundsman pulls out his tape: 20.12 m. Three different answers for one pitch, and nobody made a mistake.
To measure a quantity is to compare it with a chosen, internationally accepted reference standard called a unit. The result is always a number together with a unit: 20.12 m means "20.12 times the length called a metre". Change the unit and the number changes with it.
Measure the pitch in different units.
Every dot lands on the purple curve n = 20.12 m ÷ u: a unit twice as big gives a number half as big, because n × u is the length of the pitch, which never changes. That is why a number without its unit says nothing. "The pitch is 100" could mean 100 hand spans or 100 metres. (A cricket pitch is exactly 22 yards, an old surveyors' unit called a chain.)
Base and Derived Quantities
There are a great many physical quantities, but we need only a few units, because the quantities are related to one another. A small set of fundamental or base quantities get units of their own, the base units. Every other quantity is a combination of base quantities, and its unit, a derived unit, is the same combination of base units: speed is length ÷ time, so its unit is m ÷ s = m s⁻¹. The base units and the derived units together form a system of units. Sort these quantities.
Area is length × length (unit m²), volume is length³ (m³), density is mass ÷ volume (kg m⁻³), and force is mass × acceleration (kg m s⁻², called the newton). Next: which units are the base units today, and who decides?