A measurement is a number and a unit. Units are fixed by international agreement so that a kilogram is the same everywhere. One airliner ran out of fuel because a unit was mixed up.
“Bring 2” is not an instruction you can follow. Two kilograms, two litres and two packets are different amounts.
A measurement is a number together with a unit. The unit is the agreed amount you are counting in. The number says how many of those units there are. In “2 kg”, the unit is the kilogram and the number is 2.
A shopkeeper in one town uses a particular stone as his “1 kg” weight. A shopkeeper in the next town uses a different stone. What goes wrong?
The two stones almost certainly have different masses. So “2 kg of rice” is a different amount of rice in each town.
Neither customer can check the amount, because there is nothing both towns agree on to compare against. A unit is only useful if everyone measures against the same reference.
Why standards exist. With local objects as weights, two measurements of “1 kg” can differ and nobody can check which is right. A unit has to be defined by one reference that everyone agrees on.
Standard units do two separate jobs:
The system used in science worldwide is the SI, from the French Système international d’unités. It has seven base units. Four of them are the metre (length), the kilogram (mass), the second (time) and the ampere (electric current). Since 2019, each base unit is defined from a fixed constant of nature. The kilogram, for example, is defined from the Planck constant, so any well-equipped laboratory can reproduce it.
A Boeing 767 needed 22,300 kg of fuel for its flight. The fuel gauges were not working, so the ground crew measured the fuel in the tanks in litres and converted to mass using its density.
They used a density of 1.77. That number is the density in pounds per litre. The calculation needed kilograms per litre, which is 0.80. Because 1 pound is 0.4536 kg, the aircraft carried about 22,300 pounds of fuel, which is about 10,100 kg. That is less than half of what it needed.
The engines stopped at 12,500 m. The pilots glided the aircraft to a disused airfield at Gimli and landed. Nobody was killed.
In that incident, the crew did the multiplications correctly. Why did the aircraft still run out of fuel?
The number was right for one unit and used as if it were another. 1.77 is correct in pounds per litre. Treated as kilograms per litre, it gives a mass about 2.2 times too large, so too little fuel was added.
Writing the unit beside every number, at every step, makes this mismatch visible. “1.77 lb/L × litres” gives pounds, not kilograms, and the error shows.
1Why are units fixed by international agreement?
2The SI base unit of mass is the ____.
3In the Flight 143 incident, what went wrong?
4A student writes “the speed is 12”. What is missing?
5Sort each unit: is it an SI base unit or not?
6Which statement is correct?
7A student adds a length in metres to a time in seconds. What should you conclude?
Next: what scientists mean by a law, a theory and a principle.
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