Question

How to find the decimal expansion easily??

Answer 1

we can find type of decimal expansion of any division problem by a theorem.

let p/q be any rational number, if the prime factorisation of denominator q is in the form of 2^m*5^ n then the number has terminating decimal expansion else it will have a non-terminating repeating decimal expansion.36

For Ex-
1) 15/36
denominator= 36=2×2×3×3=2^2*3^2
here prime factorisation is not of form 2^m*5^m. hence it has non terminating decimal expansion.
2) 20/100
150=2*2*5*5
it has terminating decimal expansion.