Question

The decimal expansion of 39/(24×175) * 1 point Terminating Non - terminating Non - terminating and repeating An irrational number​

Answer 1

Step-by-step explanation:

Given: $\frac{39}{24 \times 175}$

To find:

The decimal expansion of given rational number is

a)Terminating

b) Non - terminating

c) Non - terminating and repeating

d) An irrational number

Solution:

Tip: Check the prime factors of denominator, when rational number is in standard form.

Step 1: Cancel common factors of numerator and denominator.

$\frac{39}{24 \times 175} = \frac{3 \times 13}{3 \times 8 \times 175}$

or

$\frac{39}{24 \times 175} = \frac{ 13}{ 8 \times 175}$

Step 2: Do prime factors of denominator.

$\frac{39}{24 \times 175} = \frac{13}{ {2}^{3} \times {5}^{2} \times 7 }$

Step 3: Compare prime factors of denominator.

If denominator of a rational number is in the form of ${2}^{n} \times {5}^{m}$ then, rational number is having terminating decimal expansion.

On comparison, it is clear that;

In the given rational number denominator is not in the standard form.

Therefore,

$\frac{39}{24 \times 175}$

is a Non-terminating recurring decimal expansion.

Option c is correct.

Final answer:

The rational number $\frac{39}{24 \times 175}$ is having non-terminating and repeating decimal expansion.

Option c is correct.

Hope it helps you.

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