Question 722043
We can worry about the minus sign later.
Let's consider {{{x}}}= 4.35777.....
{{{1000x}}}= 4357.7777...
{{{100x}}}= 435.7777...
{{{1000x-100x}}}= 4357.7777... - 435.7777...
{{{900x= 3922}}}
So {{{x=3922/900}}}.
We can simplify that fraction by dividing numerator and denominator by {{{2}}}
{{{x=1961/450}}}
It cannot be simplified any further, because 1961 and 450 have no factors in common.
So 4.35777..... ={{{1961/450}}}
and -4.35777..... = -{{{1961/450}}}