Re: Divide one big number by another big number (in head)
I don't think it's impossible to do the long division in
your head. Barring that, think of the divisor as
0.98724622 x 10^(8). Note that 0.98724622 is close to 1.
Dividing by 1-x is the same as multiplying by 1+x+x^2+...
so it's approximately the same as multiplying by about
1.013 x 10^(-8). 0.013 x 678242 is about 8800, so adding
678242 gives an estimate for 1.013 x 678242 at about 687000.
Then, 678242/98724622 is about 687000 x 10^(-8) or about
0.00687.
|