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Tuesday, January 3, 2017

Order of Magnitude Caluculations

In order to express quantitative magnitudes only approximately, the concept of order of magnitude is often employed. For example, the height of a small insect, say an ant, might be 8 x 10¯⁴ m ≈ 10¯³. We would say that the order of magnitude of the height of an ant is 10¯³m. Similarly, though the height of most people is about 2 m, we might round that off and say that the order of magnitude of the height of a person is 10⁰ m. By this we do not mean to imply that a typical height is really 1 m but that it is closer to 1 m than to 10 m or to 10¯¹m = 0.1 m. We might say that a typical human being is 3 orders of magnitude taller than a typical ant, meaning that the ratio of their heights is about 10³.

The order-of-magnitude of a given number is the nearest power of ten to which it is approximated. The operational definition for the order of magnitude (x) of a number (n) is 0.5 < n/10ͯˣ ≤ 5.

The order-or-magnitude of some numbers is given below.