Powers of Ten

The notation used to represent numbers that are integer powers of ten ise employed to ease the difficulty of mathematical operations with very large and very small numbers.

The positive powers of ten are greater than 1, and the negative powers of ten are less than 1.


1       = 10⁰                ; 1/10        = 0.1       = 10^-1
10     = 10¹                ; 1/100     = 0.01     = 10^-2
100   = 10²               ; 1/1000   = 0.001   = 10^-3
1000 = 10³              ; 1/10000 = 0.0001 = 10^-4


Note that any quantity to the zero power is 1 (x⁰ = 1 , 1000⁰ = 1)

10,000.0 = 10⁺⁴
0.00001  = 10^-5

The shifting a power of ten from the denominator to the numerator, or reverse, requires simply changing the sign of the power:       1 / 10ⁿ  =  10^-n   ;   1/ 10^-n  = 10<sup>n


The product of powers of ten:</sup>

        10ⁿ x 10^{m =} 10^n+m

The division of powers of ten:

      10ⁿ  / 10^m  = 10<sup>n-m



The power of powers of ten:</sup>
       (10ⁿ)^m  = 10^nm