from the linked Wikipedia article:
The neat coincidence that 2^10 is nearly equal to 10^3 provides the basis of a technique of estimating larger powers of 2 in decimal notation. Using 2^10a+b ≈ 2b10^3a is fairly accurate for exponents up to about 100. For exponents up to 300, 3a continues to be a good estimate of the number of digits.
For example, 2^53 ≈ 8×10^15. The actual value is closer to 9×10^15.
(http://www.amazon.co.uk/Penguin-Book-Curious-Interesting-Num...)
For example, 2^53 ≈ 8×10^15. The actual value is closer to 9×10^15.