If (3.14159...) is non-terminating and non-repeating, what type of number is it?
Answer and explanation
Correct answer: Irrational real number
The defining decimal criterion is that a rational number has a terminating or eventually repeating decimal expansion. A decimal that continues forever without any repeating block cannot be expressed as p/q, where p and q are integers and q is nonzero; it is therefore irrational. Since its decimal value is defined on the number line, it is still a real number. Thus the stated number is an irrational real number, making option B correct. It is not rational because the decimal neither terminates nor repeats. It is not a whole number, since whole numbers are 0, 1, 2, … and have no fractional part, and it is certainly not undefined merely because its expansion is infinite.
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What is the correct answer to this question?
Irrational real number
Why is this the correct answer?
The defining decimal criterion is that a rational number has a terminating or eventually repeating decimal expansion. A decimal that continues forever without any repeating block cannot be expressed as p/q, where p and q are integers and q is nonzero; it is therefore irrational. Since its decimal value is defined on the number line, it is still a real number. Thus the stated number is an irrational real number, making option B correct. It is not rational because the decimal neither terminates nor repeats. It is not a whole number, since whole numbers are 0, 1, 2, … and have no fractional part, and it is certainly not undefined merely because its expansion is infinite.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Number Systems. Topic: Irrational numbers.
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