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Which of the following is the decimal...

Which of the following is the decimal expansion of an irrational number

A

`4.561`

B

`0.bar(12)`

C

`5.010010001...`

D

`6.03`

Text Solution

AI Generated Solution

The correct Answer is:
To determine which of the following is the decimal expansion of an irrational number, we need to understand the characteristics of irrational numbers. An irrational number is defined as a number that is non-terminating and non-repeating. Let's analyze the options step by step: 1. **Option 1: 4.561** - This number has a finite number of decimal places (it terminates). - Therefore, it is a rational number. 2. **Option 2: 0.12̅ (0.121212...)** - This number is a repeating decimal (the digits "12" repeat indefinitely). - Since it is repeating, it is also a rational number. 3. **Option 3: 5.010010001...** - This number does not have a repeating pattern. - The sequence of decimals appears as follows: 0, 1, 0, 0, 1, 0, 0, 0, 1, and so on. - Since it does not repeat and does not terminate, it is classified as non-terminating and non-repeating. - Therefore, this number is an irrational number. Based on the analysis, the correct answer is **Option 3: 5.010010001...**.
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