Question

Solve this question please

Answer 1

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...