Question

Express zero point 999999999Express 0.99999 in the form of p by q ​

Answer 1

Answer :

• Given:
• 0.9 = 0.99999…
• Let x = 0.99999……. (1)
• Here only one digit is repeating so multiply by 10 on both sides
• 10 × x = 10× 0.99999….
• 10x = 9.9999…. (2)
• On subtracting equation 1 from equation 2
• 10x- x = 9.9999…. - 0.9999….
• 9x = 9
• x = 9/ 9 = 1
• Here , 0.9 = 1
• Yes we are surprised to get an integer 1, because 0.9999…. goes on forever so there is no gap between 1 and 0.999 9... and hence they are equal