Which decimal is non-terminating and non-repeating?
Answer and explanation
Correct answer: 0.2020020002...
A decimal expansion is non-terminating and non-repeating when it continues forever without settling into a fixed repeating block. In 0.2020020002..., the gaps between successive 2s keep changing: there are increasing strings of zeroes, so no finite block repeats periodically. Therefore it is an irrational decimal, and option A is correct. In contrast, 0.2222... is repeating and equals 2/9, so it is rational. The decimals 0.75 and 1.5000 terminate; they equal 3/4 and 3/2 respectively, so they are also rational. The important distinction is that an infinite decimal need not be irrational: an infinite repeating decimal is rational. Thus one must check both conditions—no ending and no repeating pattern—rather than merely noticing the ellipsis.
Frequently asked questions
What is the correct answer to this question?
0.2020020002...
Why is this the correct answer?
A decimal expansion is non-terminating and non-repeating when it continues forever without settling into a fixed repeating block. In 0.2020020002..., the gaps between successive 2s keep changing: there are increasing strings of zeroes, so no finite block repeats periodically. Therefore it is an irrational decimal, and option A is correct. In contrast, 0.2222... is repeating and equals 2/9, so it is rational. The decimals 0.75 and 1.5000 terminate; they equal 3/4 and 3/2 respectively, so they are also rational. The important distinction is that an infinite decimal need not be irrational: an infinite repeating decimal is rational. Thus one must check both conditions—no ending and no repeating pattern—rather than merely noticing the ellipsis.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Real Numbers. Topic: Decimal expansion of rational numbers.
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