Divide one big number by another big number (in head)
 

How would I try to divide 678242 by 98724622 in my head.

Re: Divide one big number by another big number (in head)
 

I wouldn't even try getting the correct answer
I would round to workable numbers and get a close-ish estimate.
678,242 : 680,000
98,724,622 : 100,000,000

680,000 / 100,000,000
68 / 10,000 -> Bring 68 back 4 decimal places(4 zeros)
= .0068

Which may or may not be close enough to the actual answer :
0.0068700389655581563026901232399755

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.

Re: Divide one big number by another big number (in head)
 

godBoy wins. Do you see why?

Re: Divide one big number by another big number (in head)
 

Just count the number of times 98724622 goes into 678242.