Which is the correct bar notation of (0.000919191\ldots)?
Answer and explanation
Correct answer: \(0.000\overline{91}\)
The first three digits after the decimal point, 000, do not repeat. After them, the block 91 repeats: 0.000 91 91 91... Hence, the bar must be placed only over 91, giving \(0.000\overline{91}\). In \(0.00\overline{091}\), the block 091 is treated as repeating, which does not match the given decimal. Exam tip: identify the smallest repeating block before placing the bar.
Frequently asked questions
What is the correct answer to this question?
\(0.000\overline{91}\)
Why is this the correct answer?
The first three digits after the decimal point, 000, do not repeat. After them, the block 91 repeats: 0.000 91 91 91... Hence, the bar must be placed only over 91, giving \(0.000\overline{91}\). In \(0.00\overline{091}\), the block 091 is treated as repeating, which does not match the given decimal. Exam tip: identify the smallest repeating block before placing the bar.
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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