∵设S1=2.23434...
∴10S1=22.343434...
∵1000S1=2234.343434...
∴(1000-10)S1=2212
990S1=2212
S1=2212/990
∵设S2=0.9898...
∴100S2=98.989898...
∴(100-1)S2=98
S2=98/99
∴(2.234343...-0.989898)/11
=(S1-S2)/11
=(1232/990)/11
=112/990=0.11131313...(13循环)
∵设S1=2.23434...
∴10S1=22.343434...
∵1000S1=2234.343434...
∴(1000-10)S1=2212
990S1=2212
S1=2212/990
∵设S2=0.9898...
∴100S2=98.989898...
∴(100-1)S2=98
S2=98/99
∴(2.234343...-0.989898)/11
=(S1-S2)/11
=(1232/990)/11
=112/990=0.11131313...(13循环)