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Which fractions give terminating decimals

Which fractions give terminating decimals

IP 1
7 marks
  1. Express \(0.\dot{2}\dot{7}\) as a fraction in its simplest form.[2]
  2. Express \(0.2\dot{1}\dot{8}\) as a fraction in its simplest form.[2]
  3. Using prime factorisation, explain why your answer to part (b) cannot be written as a terminating decimal, but \(\dfrac{7}{40}\) can. Write \(\dfrac{7}{40}\) as a decimal.[3]

Solution:

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Answer:(a) \(\dfrac{3}{11}\) (b) \(\dfrac{12}{55}\) (c) \(55=5\times11\) has the prime factor \(11\), which cannot divide a power of \(10\); \(40=2^3\times5\), so \(\dfrac{7}{40}=0.175\)

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