Arthur D. answered 05/30/20
Forty Year Educator: Classroom, Summer School, Substitute, Tutor
here's another solution
0.22222...
x=0.22222...
multiply both sides by 10 because only 1 digit repeats
10x=2.22222...
subtract equation 1 from equation 2
10x=2.22222...
-
x=0.22222...
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9x=2 (the decimal parts are eliminated)
x=2/9
0.787878...
x=0.787878...
multiply both sides by 100 because 2 digits repeat
100x=78.787878...
subtract equation 1 from equation 2
100x=78.787878...
-
x= 0.787878...
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99x=78 (the decimal parts are eliminated)
x=78/99
simplify
x=26/33