Which is the correct bar notation of (0.0181818...)?
Answer and explanation
Correct answer: (0.0overline{18})
The governing idea is recurring-decimal notation: a bar is placed only over the digits that repeat indefinitely. In 0.0181818..., the first digit after the decimal point is 0 and it is nonrepeating. After that, the block 18 repeats: 0.0 18 18 18 ... Therefore the correct notation is 0.0 overline{18}, option C. Option A incorrectly includes the initial nonrepeating 0 and changes the repeating block; option B treats only 8 as repeating, although every 1 is followed by 8; and option D incorrectly makes the first 0 part of the repetition. Careful separation of the nonrecurring prefix from the recurring cycle identifies C unambiguously.
Frequently asked questions
What is the correct answer to this question?
(0.0overline{18})
Why is this the correct answer?
The governing idea is recurring-decimal notation: a bar is placed only over the digits that repeat indefinitely. In 0.0181818..., the first digit after the decimal point is 0 and it is nonrepeating. After that, the block 18 repeats: 0.0 18 18 18 ... Therefore the correct notation is 0.0 overline{18}, option C. Option A incorrectly includes the initial nonrepeating 0 and changes the repeating block; option B treats only 8 as repeating, although every 1 is followed by 8; and option D incorrectly makes the first 0 part of the repetition. Careful separation of the nonrecurring prefix from the recurring cycle identifies C unambiguously.
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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