Order of Magnitude

Order of Magnitude

Very large and very small numbers can be hard to picture or write out. Some counting systems use terms corresponding to one, two, and “many”.[[26]] Scientific measurements, from the mass of a cell to the size of a galaxy, require a way to compare quantities across much wider scales.

Orders of magnitude are a form of notation used to represent large or small numbers in a compact fashion. To say a number is an order of magnitude larger than another number is to say that it is 10 times larger (a power of 10). To say it is an order of magnitude smaller means it is .10 the size. So, 10 is an order of magnitude smaller than 100, and 1,000 is an order of magnitude larger than the latter. We represent numbers between 0 and 1 with negative orders of magnitude. Scientific notation expresses a number as a coefficient multiplied by a power of 10. Science, mathematics, and engineering are disciplines for which this form of notation can be crucial.

One reason orders of magnitude are useful is that they enable us to make comparisons between numbers to give them context, such as stating how many orders of magnitude greater the weight of Earth is than the weight of a car. We also use powers of ten when handling imprecise numbers and making estimations.

In our day-to-day lives, we might easily be able to imagine a group of twenty people, but what would a crowd of one million look like? We can picture a thousand dollars in one-dollar or one-hundred-dollar bills, but how big would a stack of a billion dollars be? If we sacrifice perfect accuracy, learning to conceptualize orders of magnitude can help us compare numbers. For instance, spending a dollar a second, it would take you just over eleven days to spend a million dollars and about thirty-two years to spend a billion. The difference between the two is three orders of magnitude.

The Richter scale is an earthquake measurement system using orders of magnitude. Created by seismologists Charles F. Richter and Beno Gutenberg, it estimates earthquake magnitude from recorded seismic waves and was designed with the Southern California region in mind.[[27]] Although other systems are in use, “Richter scale” tends to serve as an umbrella term for any means of categorizing and comparing earthquakes by magnitude. Using orders of magnitude is a shortcut for showing the size difference between seismic events.

Magnitude scales can include values below 0; they have no fixed upper limit at 10. The account reports no recorded earthquake measuring 10 or more. A unit increase corresponds to ten times the measured wave amplitude, after relevant corrections, and approximately thirty-two times the energy release. Damage also depends on depth, distance, local ground conditions, and buildings. The account identifies the Chile earthquake of 1960, with magnitude 9.5, as the largest recorded event. That large-event value should not be read as a local Richter-scale measurement. Many small earthquakes can be detected instrumentally without being felt. The annual frequency estimates cited are about 1.3 million between magnitudes 2 and 2.9, compared with roughly one at 8 or higher; these are averages, not limits on a particular year.[[28]]

As Richter himself explained in his original paper on the topic:

Precision in this matter was neither expected nor required. What was looked for was a method of segregating large, moderate, and small shocks, which should be based directly on instrumental indications, and thus might be freed from the uncertainties of personal estimates or the accidental circumstances of reported effects.[[29]]

Comparing the destructive potential of earthquakes going up the Richter scale is one tool for understanding orders of magnitude.