How is (0.0767676\ldots) written in bar notation?
Answer and explanation
Correct answer: \(0.0\overline{76}\)
In \(0.0767676\ldots\), the first digit after the decimal point, \(0\), occurs only once. After that, the block \(76\) repeats: \(0.0\,76\,76\,76\ldots\). Therefore, the bar is placed only over \(76\), giving \(0.0\overline{76}\). Option A incorrectly treats \(076\) as the repeating block. Exam tip: Before placing a bar, identify the shortest block of digits that repeats continuously.
Frequently asked questions
What is the correct answer to this question?
\(0.0\overline{76}\)
Why is this the correct answer?
In \(0.0767676\ldots\), the first digit after the decimal point, \(0\), occurs only once. After that, the block \(76\) repeats: \(0.0\,76\,76\,76\ldots\). Therefore, the bar is placed only over \(76\), giving \(0.0\overline{76}\). Option A incorrectly treats \(076\) as the repeating block. Exam tip: Before placing a bar, identify the shortest block of digits that repeats continuously.
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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