Repeating Decimal 1

Express 2.5737373737373…. as a fraction of the form p/q

Solution: 2.5737373737373… means the decimal part 73 repeats itself

Let x = 2.573737373… (i)

10x = 25.73737373… (ii)

1000x = 2573.737373… (iii)

Subtracting (ii) from (iii), we get

1000x – 10x = (2573.737373) – (25.737373…)

i.e., 990x = 2548

Therefore, x = 2548/990 = 1274/495