Question 459062
{{{ 2.014141414}}}..... = 
{{{2 + .1*.14141414}}}.....
Looking only at the {{{.14141414}}}.....
I'll say:
(1) {{{y = .14141414}}}.....
(2) {{{ 100y = 14.14141414}}}.....
Subtract (1) from (2)
(2) {{{ 100y = 14.14141414}}}.....
(1) {{{y = .14141414}}}.....
{{{ 100y - y = 14 }}}
{{{ 99y = 14 }}}
{{{ y = 14/99 }}}
Now I can say:
{{{2.014141414}}}..... = {{{ 2 + .1*(14/99) }}}
{{{2.014141414}}}..... = {{{ 2 + 14/990 }}}
{{{2.014141414}}}..... = {{{ 1994/990 }}}
It is rational