A=0,9999999999....
=>10A=9,9999999999...
=>10A-A=9,999999999....-0,9999999999....
=>9A=9
=>A=1
=>0,(9)=1
ĐẶt 0,(9) = A
10A = 9,(9) = 9 + 0,(9)
10A - A = 9 + 0,(9) - 0, (9 )
9A = 9
A = 1
0,99999... =9 x 0,11111... = 9 x \(\frac{1}{9}\) = \(\frac{9}{9}\)
Vậy 0.9999...=\(\frac{9}{9}\)