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Friday, February 4, 2011

An interesting fact about the powers of 10



There seems to be only 11 powers of ten that are products of 2 integers without any zero digits.



10 ^ 0     =                      1 * 1
10 ^ 1     =                      2 * 5
10 ^ 2     =                      4 * 25
10 ^ 3     =                      8 * 125
10 ^ 4     =                      6 * 625
10 ^ 5     =                    32 * 3125 
10 ^ 6     =                    64 * 15625
10 ^ 7     =                  128 * 78125
10 ^ 9     =                  512 * 1953125 
10 ^ 18   =             262144 * 3814697265625 
10 ^ 33   =      8589934592 * 116415321826934814453125

6 comments:

  1. 10^n = (2*5)^n = 2^n * 5^n

    So, all powers of 10 can be divided into powers of 2 and 5 !!

    why 10^8 has been left = 2^8 * 5^ 8 ??

    ReplyDelete
    Replies
    1. Dr. Sathya.. Thanks for ur comments..I think you have missed to read the highlighted words...product of two numbers WITHOUT ANY ZERO DIGITS.
      5^8 = 390625

      Delete

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