The decimal (8.03003000300003…) can represent which type of number?
Answer and explanation
Correct answer: Irrational
The governing classification of decimal numbers is as follows: a terminating decimal is rational, a non-terminating decimal with a fixed repeating block is rational, and a non-terminating decimal with no repeating pattern is irrational. In 8.03003000300003…, the groups of zeros between the 3s keep changing in length: one zero, then two, then three, and so on. There is therefore no fixed finite block that repeats indefinitely. The decimal does not terminate and is non-repeating, so it represents an irrational number. Option C is correct. It cannot be a terminating rational or an integer because digits continue forever, and it is not a recurring rational because no stable repeating cycle appears.
Frequently asked questions
What is the correct answer to this question?
Irrational
Why is this the correct answer?
The governing classification of decimal numbers is as follows: a terminating decimal is rational, a non-terminating decimal with a fixed repeating block is rational, and a non-terminating decimal with no repeating pattern is irrational. In 8.03003000300003…, the groups of zeros between the 3s keep changing in length: one zero, then two, then three, and so on. There is therefore no fixed finite block that repeats indefinitely. The decimal does not terminate and is non-repeating, so it represents an irrational number. Option C is correct. It cannot be a terminating rational or an integer because digits continue forever, and it is not a recurring rational because no stable repeating cycle appears.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Number Systems. Topic: Decimal representation.
Student feedback
Was this question useful?
👍 0 Helpful 👎 0 Not helpful
Yes 0% No 0%
0 responsesStudent Reviews
No published reviews yet.
