Question

$0.30300300030000\ldots$ number is:

• A. Rational number
• B. Irrational number
• C. Natural number
• D. Integer

Hint:

If digits follow a pattern that keeps changing (like increasing zeros or growing blocks), it is usually irrational because repetition never stabilizes.

Answer 1

The Correct Option is B

Concept: A decimal number is classified as:
• Terminating decimal $\rightarrow$ Rational number
• Non-terminating repeating decimal $\rightarrow$ Rational number
• Non-terminating non-repeating decimal $\rightarrow$ Irrational number

Step 1: Observe the pattern of the given decimal.
The number is: \[ 0.30300300030000\ldots \] We observe the pattern after decimal:
• 3 followed by 1 zero: 30
• 3 followed by 2 zeros: 300
• 3 followed by 3 zeros: 3000
• 3 followed by 4 zeros: 30000 The number of zeros keeps increasing.

Step 2: Check termination and repetition.

• The decimal is non-terminating.
• There is no fixed repeating block (pattern keeps changing length). So it is neither terminating nor repeating. Conclusion: Since the decimal expansion is non-terminating and non-repeating, the number is: \[ \boxed{\text{Irrational number}} \]