Without actually performing the long division, state whether the following rational numbers will have a terminating decimal expansion or a non-terminating repeating decimal expansion: 77 / 210

77/210
=> 77/210 = (7× 11)/ (30 × 7) = 11/30

=> Factorising the denominator, we get,

=> 30 = 2 × 3 × 5

As you can see, the denominator is not in the form of 2^{m}× 5^{n} .Hence, 77/210 has a non-terminating decimal expansion.