0.777...         ->  7/9
0.373737...      ->  37/99
0.070707...      ->  7/99
0.627627627...   ->  627/999   ->  simplifying
0.027027027...   ->  27/999    ->  simplifying
0.00627627627... ->  627/99900 ->  simplifying
5.3627627627...  -> 5.3+0.0627627627... = 53/10+627/9990 = (53*999+627)/9990  ->  simplifying
0.7916666666...  -> (791.666...)/1000 = (791+2/3)/1000 = (791*3+2)/3000 = 2375/3000  ->  simplifying

simplifying fractions (or simplifying fractions)

M [627   ]  N [999   ]   [simplify]
627;999 => 3     627/999 -> 209/333

M [27    ]  N [999   ]   [simplify]
27;999 => 27     27/999 -> 1/37

M [627   ]  N [99900 ]   [simplify]
627;99900 => 3     627/99900 -> 209/33300


[53    ] [999   ]  [x]
    = [52947 ]  A
[A     ] [627   ]  [+]
M [A     ]  N [9990  ]   [simplify]
53574;9990 => 6     53574/9990 -> 8929/1665
            verification:
[8929  ] [1665  ]  [/]
    = [5.362762762762763 ]

M [2375   ]  N [3000 ]   [simplify]
2375;3000 => 125     2375/3000 -> 19/24