Base converter with fractions?

[Jan_D]

When I would like to express 3.142 in base 7, I would do the following.

Multiplication with 7^4 gives: 7543.942
Rounded this is: 7544

Now I am going to express this integer number in base 7:

Division of 7544 by 7^4 (=2401) gives 3+rest 341
Division of 341 by 7^3 (=343) gives 0+rest 341
Division of 341 by 7^2 (49) gives 6+rest 47
Division of 47 by 7 gives 6+ rest 5.

So 7544=3*7^4+0*7^3+6*7^2+6*7+5 and therefore 7544=30665_base7

In the beginning we multiplied with 7^4, so now we have to divide again by 7^4, which shifts the point by 4 positions, and thus gives: 3.142=3.0665_base7