Question

How do you write
1

9
as a decimal?

Answer 1

1/9 = 0.111... (repeating), often written 0.\overline{1}.

Quick checks:
- Long division: 9 into 1.000... gives 0.111...
- Geometric series: 0.111... = sum_{k=1}^\infty 10^{-k} = (1/10)/(1-1/10) = 1/9.
- Or multiply: 9 × 0.111... = 0.999... = 1, so 0.111... = 1/9.