Question

among 1/2 ,1/3, 1/4, 1/5 what is the non terminating decimal​

Answer 1

HERE IS YOUR ANSWER MATE!

The non terminating decimal is 1/3 as it is a recurring decimal and there are no factors of either 2 or 5 in denominator.

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Answer 2

The decimal representation of $\bf{ \frac{1}{ 3} }$ will be non terminating

Given :

The fractions 1/2 , 1/3 , 1/4 , 1/5

To find :

The fraction which have non terminating decimal

Concept :

$\displaystyle\sf{Fraction = \frac{Numerator}{Denominator} }$

A fraction is said to be terminating if prime factorisation of the denominator contains only prime factors 2 and 5

If the denominator is of the form

$\sf{Denominator = {2}^{m} \times {5}^{n} }$

Then the fraction terminates after N decimal places

Where N = max { m , n }

Solution :

Step 1 of 2 :

Write down the given fractions

Here the given fractions are 1/2 , 1/3 , 1/4 , 1/5

Step 2 of 2 :

Find the fraction which have non terminating decimal

For the fraction 1/2 :

Numerator = 1

Denominator = 2

Since the prime factorisation of the denominator contains only prime factors as 2

So the decimal representation is terminating

For the fraction 1/3 :

Numerator = 1

Denominator = 3

Since the prime factorisation of the denominator contains prime factor as 3

So the decimal representation is non terminating

For the fraction 1/4 :

Numerator = 1

Denominator = 4 = 2²

Since the prime factorisation of the denominator contains only prime factor as 2

So the decimal representation is terminating

For the fraction 1/5 :

Numerator = 1

Denominator = 5

Since the prime factorisation of the denominator contains only prime factor as 5

Hence the decimal representation of $\bf{ \frac{1}{ 3} }$ will be non terminating

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