Question

64/465 is terminating or non terminating ​

Answer 1

Answer:

non terminating

64÷465

= 0.1376344086021

Answer 2

Solution :-

A Rational Number $\mathtt{\dfrac{p}{q}}$ is expressible as a Terminating Decimal only when Prime Factors are 2 and 5 only.

$\begin{gathered} \end{gathered}$

According to the Question,

Denominator of $\mathtt {\dfrac{64}{465}}$ is 465.

And, $\mathtt{465 = 3 \times 5 \times 31}$.

$\begin{gathered} \end{gathered}$

Thus, 465 has Prime Factors 3 and 31, which is other than 2 and 5.

∴ $\mathtt {\dfrac{64}{465}}$ is a Non - Terminating Decimal.

$\begin{gathered} \end{gathered}$

Additional Information :-

Decimal Representation of Rational Numbers :-

Every Rational Number $\mathtt{\dfrac{p}{q}}$ can be expressed as a Decimal. On dividing p and q , two possibilities arise :

$\begin{gathered} \end{gathered}$

$\bullet$ The Remainder becomes 0 and the Division concludes after a finite number of steps. The Decimal Expansion terminates or ends.

$\begin{gathered} \end{gathered}$

$\bullet$ The Remainder never becomes 0 and a Repeating string of Remainders is obtained. We get a Digit or a Block of Digits repeating in the Decimal Expansion.