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Example 8 - Show that 1.272727…… = 1.(27) can be expressed - Expressing decimal in p/q


Transcript

Example 8 Show that 1.272727…… = 1.(27) ̅ can be expressed in the form 𝑝/𝑞 , where p and q are integers and q ≠ 0. Let x = 1.(27) ̅ = 1.272727… Multiplying equation (1) with 100 100x = 100 × (1.272727…) 100x = 127.2727… Subtracting (2) from (1) i.e. (2) – (1) 100x – x = 127.2727… – 1.272727… 99x = 126.0000… x = 126/99 x = 14/11 Thus, 1.(27) ̅ = 14/11

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Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He provides courses for Mathematics from Class 9 to 12. You can contact him here.
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