Question

With out actually performing the long division,find if 23\2048 will have terminating or non terminating repeating decimal expansion.give reason for your answer

Answer 1

Step-by-step explanation:

23 / 2048

===> 23 / 2¹¹

Multiply and divide with 5¹¹ on both sides

23 / 2¹¹ × 5¹¹ / 5¹¹

23 × 5¹¹ / 10¹¹

23 × 48,828,125 / 100,000,000,000

1,123,046,875 / 100,000,000,000

===> 0.01123046875

It is a terminating decimal

Reason :-

❤️If the prime factorisation of the denominator is in the form of 2n , 5m then it becomes terminating decimal .