What type of decimal expansion does \(\frac{1}{7}\) have?
Answer and explanation
Correct answer: Non-terminating recurring
\(\frac{1}{7}=0.142857142857\ldots\), in which the block 142857 repeats indefinitely. Hence, its decimal expansion is non-terminating recurring. A decimal terminates only when, in lowest form, the denominator has prime factors 2 and 5 only; here the denominator is 7. A non-terminating non-recurring decimal represents an irrational number, whereas \(\frac{1}{7}\) is rational. Exam tip: First reduce a fraction to lowest terms, then inspect the prime factors of its denominator.
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What is the correct answer to this question?
Non-terminating recurring
Why is this the correct answer?
\(\frac{1}{7}=0.142857142857\ldots\), in which the block 142857 repeats indefinitely. Hence, its decimal expansion is non-terminating recurring. A decimal terminates only when, in lowest form, the denominator has prime factors 2 and 5 only; here the denominator is 7. A non-terminating non-recurring decimal represents an irrational number, whereas \(\frac{1}{7}\) is rational. Exam tip: First reduce a fraction to lowest terms, then inspect the prime factors of its denominator.
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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