Question

Write the condition satisfied by 455, so that 455 /64 has a non-terminating repeating decimal expansion.

Answer 1

the condition satisfying it will be
if the denominator will have factors other than 2 and 5 the decimal expansion will have a non-terminating repeating

Answer 2

Answer:

$\frac{455}{64}=7.109375$ is a terminating number.

Condition is 455 should be in denominator

$\frac{64}{455}=0.1406593407..$

Step-by-step explanation:

To Write : The condition satisfied by 455, so that $\frac{455}{64}$ has a non-terminating repeating decimal expansion.

Solution :

Since $\frac{455}{64}=7.109375$ is a terminating number.

So, to satisfy 455 the condition of a number is $\frac{64}{455}$

If number in denominator is in the form $2^m \times 5^n$  then it is terminating,

In this case,

$\frac{64}{455}=\frac{2^6}{5^1\times 7^1\times 13^1}$

Here it is non terminating as 2 is not in denominator.

When we solve $\frac{64}{455}=0.1406593407..$

Hence it is non repeating and non-terminating.