Early in my last year of university, my most energetic geology professor asked his class to give the rate of drift for Earth’s tectonic plates. The other students and I – exercising the habits of memorization that come from three years of education in the natural sciences – looked to the ceiling or floor and began to recall previous classes. Did he want the faster drift rates of the Pacific plate (7-12 cm/year) or the slower rates of the North American plate (2-4 cm/year)? The Antarctic plate hardly moves at all. . .

The professor waved his arms enthusiastically and told us to stop thinking. “Orders of magnitude only!” he explained. “Let’s call it 1 cm/year. What about rates of mountain uplift in active regions, like the Himalayas and New Zealand?” The answer, to an order of magnitude, was 0.1 cm/year.

Now his point was obvious: plates drift faster than mountains rise, but both move at similar speeds. This relationship – normally hidden behind numbers like 7.3 and 0.4 – was suddenly clear in the comparison of 1 and 0.1. We had lost some precision, but had gained clarity, which we would easily remember.

The professor waved his arms enthusiastically and told us to stop thinking. “Orders of magnitude only!” he explained. “Let’s call it 1 cm/year. What about rates of mountain uplift in active regions, like the Himalayas and New Zealand?” The answer, to an order of magnitude, was 0.1 cm/year.

Now his point was obvious: plates drift faster than mountains rise, but both move at similar speeds. This relationship – normally hidden behind numbers like 7.3 and 0.4 – was suddenly clear in the comparison of 1 and 0.1. We had lost some precision, but had gained clarity, which we would easily remember.

An order of magnitude is a group of measurements (all of the same type) that fall within one power of ten. So 2 and 7 are the same order of magnitude, but 12 is one order of magnitude greater and 70,000 is four greater. Each could be approximated as 10^{0}, 10^{0}, 10^{1}, and 10^{4}, respectively. This simplicity makes orders of magnitude excellent for quickly comparing very large (and very small) numbers.