Question

show that 1242/49 is a non terminating repeating decimal​

Answer 1

Answer:

Proof:

Step-by-step explanation:

1242/49

1242/7^2

In order for a number to be terminating, the denominator should be in the form of 5^n x 2^m

Since the denominator in 1242/49 is not in the form of 5^n x 2^m, 1242/49 is nob terminating and repeating

Answer 2

1242/49 is a non terminating repeating decimal is proved

Given : The number 1242/49

To prove : 1242/49 is a non terminating repeating 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 fraction

The given fraction is 1242/49

Step 2 of 2 :

Check whether terminating or not

Numerator = 1242

Denominator = 49

Prime factorisation of denominator is

49 = 7 × 7

Since the prime factorisation of the denominator contains prime factor as 7 only

So the decimal expansion of the given fraction is non terminating repeating decimal

Hence proved

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