Convert 2.4(178)..  to p/q form where p and q are integers and q ≠ 0

Last updated at July 21, 2026 by

Convert 2.4(178)..  to p/q form where p and q are integers and q ≠ 0

Convert 2.4(178)..  to p/q form where p and q are integers and q ≠ 0 - Part 2

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Convert 2.4(178) ̅ to p/q form where p and q are integers and q ≠ 0 Let x = 2.4178178178….. Multiplying equation (1) with 1000 1000x = 1000 × (2.4178178178…) 1000x = 2417.8178178… Subtracting (2) from (1) i.e. (2) – (1) 1000x – x = 2417.8178178… – 2.4178178178….. 999x = 2415.4 Since there is bar over 3 digits, we multiply by 1000 2417.8178178… 2.4178178… 999x = 24154/10 x = 𝟐𝟒𝟏𝟓𝟒/𝟗𝟗𝟗𝟎 Thus, 2.4(178) ̅ = 𝟐𝟒𝟏𝟓𝟒/𝟗𝟗𝟗𝟎

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