Question

Find the decimal expansion of 13/3125 without actual

Answer 1

we see 3125 = 5*5*5*5*5.
now
13/3125= 13/5^5
= 13 * 2^5/5^5 * 2^5
= 13*32/100000. (10 = 2*5. 100 =2^2*5^2...)
= .00416 (plz check the calculation)
therefore we have divided 13 by 3125 without actual calculation...