Question

How do we write 0.1234 (all 4 digits repeating) as a fraction?

Answer 1

$let \: y = 0.1234........... \\ y = 0.12341234....... - -- - 1eq. \\ multiply \: both \: sides \: by \: 10000 \\ 10000 \times y = 10000 \times 0.12341234... \\ 10000y = 1234.1234.... - - - - 2eq. \\ subtract \: eq.1 \: from \: eq.2 \\ 10000y - y = 1234.1234..... - 0.1234.... \\ 9999y = 1234 \\ y = \frac{1234}{9999}$