How do you do scientific notation in another base other than base 10?

Answer 1

Suppose you want to express the number N in base b (b > 1).

Assume, for the moment that N > 0. If N < 0 the method is the same, you just stick a minus sign in front. The reason for the assumption is that step one is not defined if N < 0. I would have had to define everything in terms of abs(n) and then disentangle it at the end.

The first step is to find logbN = log10N/log10b

this will be some real number k such that N = bk.

The next step is to find the largest integer, i which is less than or equal to k and then let j = k - i.

If k > 0 then i is the integer part of k and j is the fractional part, 0 ≤ j < 1.

If k < 0 then i is the integer before k and j is the positive increment to it. Again, 0 ≤ j < 1

[The key point here is that if, for example, k = -3.2 then i = -4 and j = +0.8]

Then N = bk = bi+j = bj+i = bj * bi

The final step is to calculate bj = a

and, since 0 ≤ j < 1 you have 0 ≤ bj < b

then N = a*bi is the scientific notation for N in base b.