The decimal (6.03003000300003…) can represent which type of number?
Answer and explanation
Correct answer: Irrational
A rational number has a decimal expansion that either terminates or continues with a fixed repeating block. In 6.03003000300003…, the groups of zeros between successive 3s keep increasing, so there is no fixed block that repeats forever. The decimal is non-terminating and non-recurring, which is the characteristic decimal form of an irrational number. Therefore option C is correct. Option A is unsuitable because the decimal does not end. Option B is unsuitable because no constant cycle repeats. Option D is also impossible because an integer has no nonzero digits after the decimal point.
Frequently asked questions
What is the correct answer to this question?
Irrational
Why is this the correct answer?
A rational number has a decimal expansion that either terminates or continues with a fixed repeating block. In 6.03003000300003…, the groups of zeros between successive 3s keep increasing, so there is no fixed block that repeats forever. The decimal is non-terminating and non-recurring, which is the characteristic decimal form of an irrational number. Therefore option C is correct. Option A is unsuitable because the decimal does not end. Option B is unsuitable because no constant cycle repeats. Option D is also impossible because an integer has no nonzero digits after the decimal point.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Number Systems. Topic: Decimal representation.
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