In simplest form, what type of decimal expansion will ( \frac{132}{484} ) have?
Answer and explanation
Correct answer: Non-terminating recurring
First reduce the fraction before deciding the type of decimal expansion. The numerator and denominator have a common factor 44: \\(\frac{132}{484}=\frac{3}{11}\\). The simplified denominator is 11, which is a prime factor other than 2 or 5. A rational number whose simplified denominator contains such a factor has a non-terminating recurring decimal expansion.
For confirmation, division gives \\(\frac{3}{11}=0.272727\ldots\\), where the block 27 repeats endlessly. Thus option C is correct. It is important not to judge the original denominator 484 without simplification, because common factors may disappear. Here, however, the remaining factor 11 clearly prevents termination and produces repetition.
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What is the correct answer to this question?
Non-terminating recurring
Why is this the correct answer?
First reduce the fraction before deciding the type of decimal expansion. The numerator and denominator have a common factor 44: \\(\frac{132}{484}=\frac{3}{11}\\). The simplified denominator is 11, which is a prime factor other than 2 or 5. A rational number whose simplified denominator contains such a factor has a non-terminating recurring decimal expansion.
For confirmation, division gives \\(\frac{3}{11}=0.272727\ldots\\), where the block 27 repeats endlessly. Thus option C is correct. It is important not to judge the original denominator 484 without simplification, because common factors may disappear. Here, however, the remaining factor 11 clearly prevents termination and produces repetition.
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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