If a decimal is non-terminating and non-repeating, what type of number is it?
Answer and explanation
Correct answer: Irrational number
The governing classification rule is that a rational number has a decimal expansion that either terminates or repeats in a fixed periodic pattern. An irrational number has a decimal expansion that is non-terminating and non-repeating. Thus, if digits continue indefinitely and no block of digits repeats regularly, the number cannot be written as p/q where p and q are integers and q is non-zero. Therefore option A is correct. A rational number may look long, but it must eventually terminate or repeat; an integer is a special rational number, and a terminating decimal is explicitly the opposite of the description.
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What is the correct answer to this question?
Irrational number
Why is this the correct answer?
The governing classification rule is that a rational number has a decimal expansion that either terminates or repeats in a fixed periodic pattern. An irrational number has a decimal expansion that is non-terminating and non-repeating. Thus, if digits continue indefinitely and no block of digits repeats regularly, the number cannot be written as p/q where p and q are integers and q is non-zero. Therefore option A is correct. A rational number may look long, but it must eventually terminate or repeat; an integer is a special rational number, and a terminating decimal is explicitly the opposite of the description.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Real Numbers. Topic: Irrational numbers.
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