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Let x = 0.1232323... --- eq(2)
Here periodicity = 2
So multiply by 100 on both the sides
100 * x = 100 * 0.1232323..
100x =12.3232323... ---- eq(2)
Subtract eq(1) from eq(2)
i.e, eq(2) - eq(1)
100x = 12.323232...
-x = 0.12323....
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99x = 12.2
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x = 12.2/99
x = 122/990 (to eliminate the decimal I multiplied the numerator and denominator by 10)
x = 61/495 (numerator and denominator have 2 in common so, I cancelled them)
So x = 61/495 (61 and 496 are coprimes so it is the simplest form)
61/495 is p/q form of 0.1232323...
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