|Cardinal||one thousand twenty-four|
(one thousand twenty-fourth)
|Divisors||1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024|
Approximation to 1000
The neat coincidence that 210 is nearly equal to 103 provides the basis of a technique of estimating larger powers of 2 in decimal notation. Using 210a+b ≈ 2b103a 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, 253 ≈ 8×1015. The actual value is closer to 9×1015.
In the case of larger exponents, the relationship becomes increasingly inaccurate, with errors exceeding an order of magnitude for a ≥ 97. For example:
In measuring bytes, 1024 is often used in place of 1000 as the quotients of the units byte, kilobyte, megabyte, etc. In 1999, the IEC coined the term kibibyte for multiples of 1024, with kilobyte being used for multiples of 1000.
Special use in computers
- Bryan Bunch, The Kingdom of Infinite Number. New York: W. H. Freeman & Company (2000): 170