Question

2. Write down the decimal expansions of those rational numbers in Question 1 above
which have terminating decimal expansions.
The following real numbers have decimal expansions as given below. In each case, 64/455​

Answer 1

Answer

64/455 has non-terminating decimal expansion.

Explanation

If the denominator of a fraction has its prime factors as only 2s and 5s, i.e. of the form 2ᵐ×5ⁿ, where m and n are positive integers, then the fraction has terminating decimal expansion.

64/455

Denominator of the fraction 64/455 is 455

Prime factorised form of 455:

455 = 5 × 7 × 13

Prime factorisation of 455 is not of the form 2ᵐ×5ⁿ, So 64/455 has non-terminating decimal expansion.