Question

Which of the following is a non terminating repeating ? (a) 3/8 (b) 7/80 (c) 64/455 (d) 124/625.

Answer 1

Answer:

3/8

=3/2√2

=1•5/√2

denominator is on the form of root

therefore,it is irrational no.

so,it is non terminating repeating.

Answer 2

Option c - $\dfrac{64}{455}$ is non terminating repeating.

Step-by-step explanation:

To find : Which of the following is a non terminating repeating ?

Solution :

The number will terminate is denominator is in form of $2^m\times 5^n$.

So,

(a) $\frac{3}{8}$

$\frac{3}{8}=\frac{3}{2^3}$

Multiply and divide by $5^3$,

$\frac{3}{8}=\frac{3\times 5^3}{2^3\times 5^3}$

$\frac{3}{8}=\frac{375}{10^3}$

$\frac{3}{8}=0.375$

It will terminate.

(b) $\frac{7}{80}$

$\frac{7}{80}=\frac{7}{2^4\times 5}$

Multiply and divide by $5^3$,

$\frac{7}{80}=\frac{7\times 5^3}{2^4\times 5^4}$

$\frac{7}{80}=\frac{875}{10^4}$

$\frac{7}{80}=0.0875$

It will terminate.

(c) $\frac{64}{455}$

$\frac{64}{455}=\frac{64}{5\times 7\times 13}$

It will non-terminating repeating.

(d) $\frac{124}{625}$

$\frac{124}{625}=\frac{124}{5^4}$

Multiply and divide by $2^4$,

$\frac{124}{625}=\frac{124\times 2^4}{2^4\times 5^4}$

$\frac{124}{625}=\frac{1984}{10^4}$

$\frac{124}{625}=0.1984$

It will terminate.

#Learn more

The decimal expansion of the rational number 33/22.5 will terminates after .How many places of decimal

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