Convert 0.123333 .. to p/q form where p and q are integers and q ≠ 0

Last updated at July 27, 2026 by

Convert 0.123333 .. to p/q form where p and q are integers and q ≠ 0

Convert 0.123333 .. to p/q form where p and q are integers and q ≠ 0 - Part 2

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Convert 0.123 ̅ to p/q form where p and q are integers and q ≠ 0 Let x = 0.12333….. Multiplying equation (1) with 10 10x = 10 × (0.12333…) 10x = 1.23333… Subtracting (2) from (1) i.e. (2) – (1) 10x – x = 1.23333… – 0.123333… 9x = 1.11 Since there is bar over 3 only, (one digit) 1.23333… 0.12333… 9x = 111/100 x = 𝟏𝟏𝟏/𝟗𝟎𝟎 Thus, 0.123 ̅ = 𝟏𝟏𝟏/𝟗𝟎𝟎 0.123 ̅ = 𝟏𝟏𝟏/𝟗𝟎𝟎

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