The order of magnitude of a number is the power of 10 closest to that number.

Rule: Express the number as N x 10^n where 1 <= N < 10. If N <= 5 (some books use sqrt(10) = 3.16), the order of magnitude = n. If N > 5, the order of magnitude = n + 1.

Examples:

• 300 = 3 x 10^2, order = 2 (since 3 < 5)
• 800 = 8 x 10^2, order = 3 (since 8 > 5)
• 6.4 x 10^6 (Earth's radius in m), order = 7

JEE use: Quick estimation problems — "the ratio of X to Y is of the order of 10^?"