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Order of magnitude
Scale of numbers with a fixed ratio
Order of magnitude
In a ratio scale based on powers of ten, the order of magnitude is a measure of the nearness of two figures. Two numbers are "within an order of magnitude" of each other if the ratio of the greater to the lesser is between 1 and 10. In other words, the two numbers are within about a factor of 10 of each other. For example, 1 and 1.02 are within an order of magnitude, as well as 1 and 2, 1 and 9, and 1 and 0.2. However, 1 and 15 are not within an order of magnitude, since their ratio is 15/1 = 15 > 10. The reciprocal ratio, 1/15, is less than 0.1, so the same result is obtained. Differences in order of magnitude can be measured on a base-10 logarithmic scale in "decades" (i.e., factors of ten). For example, there is one order of magnitude between 2 and 20, and two orders of magnitude between 2 and 200. Each division or multiplication by 10 is called an order of magnitude. This phrasing helps quickly express the difference in scale between 2 and 2,000,000: they differ by 6 orders of magnitude...
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