Orders of Magnitude

The order of magnitude of a number is the power of 10 that most closely approximates it. Thus, the order of magnitude estimates the scale (or size) of its value. To find the order of magnitude of a number, take the base-10 logarithm of the number and round it to the nearest integer. Then the order of magnitude of the number is simply the resulting power of 10.

The order of magnitude is simply a way of rounding numbers consistently to the nearest power of 10. This makes doing rough mental math with very large and very small numbers easier. For example, the diameter of a hydrogen atom is on the order of 10^-10 m, whereas the diameter of the Sun is on the order of 10⁹ m, so it would take roughly 10⁹/10^-10 = 10¹⁹ hydrogen atoms to stretch across the diameter of the Sun. This is much easier to do in your head than using the more precise values of 1.06×10^-10 m for a hydrogen atom diameter and 1.39×10⁹ m for the Sun's diameter, to find that it would take 1.31×10¹⁹ hydrogen atoms to stretch across the Sun's diameter. In addition to being easier, the rough estimate is also nearly as informative as the precise calculation.