Question

Write whether the rational number 7 by 75 will have a terminating decimal expansion or anon terminating repeating decimal expansion

Answer 1

The denominator of Any terminating decimal can be expressed in the form of 2*5

7/75

=> 7 / 25*3

=> 7 / 5²×3 .

As the denominator 7/75 is not expressed as product of only 2 or 5 or both. Hence, 7/75 isn't a terminating decimal.

Answer 2

$\huge\red {Hlo}$

1. The decimal expansion of a rational number always either terminates after finitely many digits or begins to repeat the same sequence of digits over and over.

2. Moreover,any repeating or terminating decimal represents a rational number.