Question

Write down the decimal expansions of the following rational numbers by writing their denominators in the form 2n 5 m , where n, m are non-negative integers: (i) 7/8 (ii) 39/500​

Answer 1

The fraction 257/5000

Since the denominator is 5000,

The factors for 5000 are:

5000=2×2×2×5×5×5×5

=23×54

257/5000=257/(23×54)

It is a terminating decimal.

So,

Let us multiply both numerator and denominator by 2, we get

257/5000=(257×2)/(5000×2)

=514/10000

=0.0514