Which decimal shows an irrational number?
Answer and explanation
Correct answer: 0.3030030003...
An irrational decimal must be non-terminating and non-repeating. Option A, 0.3030030003..., shows increasing numbers of zeros between 3s so there is no fixed repeating block; it is non-terminating and non-repeating, hence irrational. Option B (0.303030...) repeats the block “30” and is therefore rational. Options C (0.303) and D (0.3000... which equals 0.3) are terminating decimals and thus rational. Exam tip: check for termination or a fixed repeating pattern — terminating or repeating implies rational; non-terminating non-repeating implies irrational.
Frequently asked questions
What is the correct answer to this question?
0.3030030003...
Why is this the correct answer?
An irrational decimal must be non-terminating and non-repeating. Option A, 0.3030030003..., shows increasing numbers of zeros between 3s so there is no fixed repeating block; it is non-terminating and non-repeating, hence irrational. Option B (0.303030...) repeats the block “30” and is therefore rational. Options C (0.303) and D (0.3000... which equals 0.3) are terminating decimals and thus rational. Exam tip: check for termination or a fixed repeating pattern — terminating or repeating implies rational; non-terminating non-repeating implies irrational.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Polynomials. Topic: Irrational numbers and real numbers.
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