Question

The decimal representation of 7/24 is
Non terminating and non recurring

Answer 1

Answer:

Non Terminating

Step-by-step explanation:

To have a termination decimal expansion the denominator should be able to be expressed in terms 2 and 5, but in this question the denominator is in terms of 2 and 3

This 7/24 has a non Terminating decimal expansion

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Answer 2

The decimal expansion of 7/24 is non-terminating and recurring decimal expansion.

Given:

• $\frac{7}{24}$

To find:

• Decimal representation of a given rational number is terminating or non-terminating and non-recurring.

Solution:

Concept to be used:

• If a standard rational number p/q, where q ≠ 0 have terminating decimal expansion then prime factors or q are in the form $\bf {2}^{n} \times {5}^{m}$ where, n and m are positive integers.

Step 1:

Check for the given rational number.

Check the given rational number, whether it is in standard form or not, for that, check whether numerator and denominator are co-prime numbers or not.

It is clear that, 7 and 24 don't have any common factor.

So,

7 and 24 are co-prime numbers.

Thus,

7/24 is in the standard form.

Step 2:

Check the decimal expansion of rational number.

Factorise the denominator, i.e. 24

$24 = 2 \times 2 \times 2 \times 3$

$\bf 24 = {2}^{3} \times 3$

The denominator of the given rational number is not in the form ${2}^{n} \times {5}^{m}$

Thus,

The decimal expansion of 7/24 is non-terminating and recurring decimal expansion.

Learn more:

1) 3/8 will terminate after how many decimal places

https://brainly.in/question/9415547

2) After how many decimal points, numbers 5/1600 terminate ?

a)5 b)6

c)7 d)8

https://brainly.in/question/46809332

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