Question

Which of the following is an irrational number? (a) 3.14 (b)3.1414... (c)3.1444... (d)3.141141114

Answer 1

Option (d) 3.141141114 is an irrational number.
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Answer 2

3.14114114...... is an irrational number.

Option (d) is correct.

Given:

• (a) 3.14
• (b)3.1414...
• (c)3.1444...
• (d)3.141141114...

To find:

• Which of the above written is an irrational number?

Solution:

Definition/Concept to be used:

1. Rational number: It's decimal expansion is either terminating or non-terminating repeating.
2. Irrational number: It's decimal expansion is neither terminating nor non-terminating repeating.

Case 1:

Check for option a) 3.14

it is terminated decimal expansion.

Thus,

3.14 is rational number.

Case 2:

Check for option b) 3.1414...

it is non-terminating recurring decimal expansion.

As, 14 is repeating after decimal point.

Thus,

3.1414... is rational number.

Case 3:

Check for option c) 3.1444...

it is non-terminating recurring decimal expansion.

As, 4 is repeating after decimal point.

Thus,

3.1444... is rational number.

Case 4:

Check for option d) 3.14114114...

it is non-terminating non-recurring decimal expansion.

Thus,

3.14114114...... is an irrational number.

Option (d) is correct.

Remark:

* mistake corrected in option 4, without (...) the number is terminating decimal, thus becomes rational.

Learn more:

1) The number 0.737337333….. is rational or irrational

https://brainly.in/question/18049996

2) Which of the following is an irrational number? 1 (a) 3.245245 (b) 3.245 (c) 2.345245… (d) 3.2452245522245

https://brainly.in/question/47468091

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