Chapter 1 — Units and Measurement

In July 1983 a brand-new Boeing 767 ran both engines dry halfway across Canada. The fuel gauges were out of order, so the crew measured the fuel with a dipstick, in litres, and converted it to mass with a density. The number they used, $1.77$, was the density of jet fuel in pounds per litre; the aircraft's systems worked in kilograms, where the right number is $0.803$. Every multiplication was correct. The units were not, and the aircraft left with less than half the fuel it needed. The pilots glided it down safely onto an old airfield at Gimli, Manitoba.

Sixteen years later, NASA lost the Mars Climate Orbiter because one piece of software reported thruster impulses in pound-force seconds while another expected newton seconds. Physics is a quantitative science: a law such as $F=ma$ only means something when every symbol carries a number and a unit, written to a sensible precision, and when both sides of the equation describe the same kind of thing. This chapter gives you those three tools — units, significant figures and dimensions — and you will use them on every page that follows.

Sections in this chapter