Question

Decimal representation of a rational

number cannot be

(a) Terminating

(b) non-terminating

(c) non-terminating repeating

(d) non-terminating non-repeating​

Answer 1

Answer:

The decimal representation of a rational number cannot be: non-terminating

Answer 2

Answer:

non-terminating non-repeating.

Step-by-step explanation:

For all rational numbers of the form $\fbox{${\frac{p}{q}{\mathrm{(}}{q}\mathrm{\ne}{0}{\mathrm{)}}}$}$, on division of p by q, two things may happen:

1. The remainder becomes zero and the decimal expansion terminates or ends after a finite number of steps.For example, $\fbox{${\frac{1}{4}\mathrm{{=}}{0}{\mathrm{.}}{\mathrm{25}}}$}$
2. The remainder never becomes zero and the remainders repeat after a certain stage forcing the decimal expansion to go on for ever. In such a case, we have a repeating block of digits in the quotient. For example:$\fbox{${\frac{1}{6}\mathrm{{=}}{0}{\mathrm{.}}{\mathrm{16666}}{\mathrm{....}}}$}$

From above, we can see that the decimal expansion of a rational number is either terminating or non-terminating repeating (recurring). Hence, we can safely conclude that the decimal expansion of a rational number should be terminating or non-terminating repeating. Hence, it can't be non-terminating non-repeating.

${}^{i \: hope \: its \: help \: you.}$