Eduprobe
Question:
Express 0.99999... in the form p/q. Are you surprised by your answer?
Solution:
Letx=0.99999⋯.. (1)Multiply eq (1) by10we get10x=9.9999⋯.. (2)Substract (1) from (2), we get⇒9x=9⇒x=11=1Here,p=1andq=1Thus,0.9999⋯=1
Letx=0.99999⋯.. (1)Multiply eq (1) by10we get10x=9.9999⋯.. (2)Substract (1) from (2), we get⇒9x=9⇒x=11=1Here,p=1andq=1Thus,0.9999⋯=1