Without actual division find whether 18/30 will have a terminating decimal expansion or a non-terminating repeating decimal - Maths - Real Numbers

Question

Without actual division find whether 18/30 will have a terminating
decimal expansion or a non-terminating repeating decimal

Varun Rawat · Accepted Answer

Dear Student,

We know that, a rational number has a terminating decimal expansion if the prime factorisation of the denominator is of the form of 2m 5n, wherem and n are non negative real numbers
Now, given number = 1830 = 35 = 320 × 51Since, the denominator is of the form of 2m 5n, where m and n are non negative real numbers, hence the given number has terminating decimal expansion
Regards