Why is 0.999...=1?| Visual and Algebraic Proof #maths

Added: 2026-05-26

The infinite decimal 0.999... is mathematically equal to 1, as there is no number between them; this can be proven through algebraic methods (let x = 0.999..., then 10x = 9.999..., so 10x - x = 9, which gives 9x = 9, so x = 1), infinite geometric series (0.999... = 9/10 + 9/100 + 9/1000 + ... = 9 × (1/10)/(1 - 1/10) = 9 × (1/10)/(9/10) = 9 × 1/9 = 1), and number-line visualization showing no gap exists between 0.999... and 1.