Which of the following is a non-terminating repeating decimal?
(a)35/14.
(b)14/35
(c)1/7
(d)7/8

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Solution

$(a) . The given number is \frac{35}{14} . Now, \frac{35}{14} = \frac{5}{2} (simplified form) Here the denominator = 2 Since the prime factorisation of the denominator is of the form of 2^{n} 5^{m}, so given number has a terminating decimal expansion . (b) . The given number is \frac{14}{35} . Now, \frac{14}{35} = \frac{2}{5} (simplified form) Here the denominator = 5 Since the prime factorisation of the denominator is of the form of 2^{n} 5^{m}, so given number has a terminating decimal expansion . (c) . The given number is \frac{1}{7} . Here the denominator = 7 Since the prime factorisation of the denominator is not of the form of 2^{n} 5^{m}, so given number has a non - terminating repeating decimal expansion . (d) . The given number is \frac{7}{8} . Here the denominator = 8 prime factorisation of 8 = 2 \times 2 \times 2 = 2^{3} Since the prime factorisation of the denominator is of the form of 2^{n} 5^{m}, so given number has a terminating decimal expansion .$

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