Question

26/2185
15632/625
368/512

these three rational numaber have terminating and non terminating decimal expansion. justify your answer..​

Answer 1

Answer:

26/2185

it will have non terminating decimal expansion as prime factorisation of 2185 contain 5*19*23 but for decimal expansion to be terminating denominator should contain 2^n and 5^m

15632/625

it will have terminating decimal expansion as prime factorisation of 625 contain 5^4 and 2^0 and for decimal expansion to be terminating denominator should contain 2^n and 5^m

368/512

it will have terminating decimal expansion as prime factorisation of 512 contain 2^9 and 5^0 and for decimal expansion to be terminating denominator should contain 2^n and 5^m