Question

How do you write 1/9
as a decimal?

Answer 1

1/9 = 0.111... (the 1 repeats forever). You can write it as 0.\overline{1}.

Quick checks:
- Long division: 1 ÷ 9 = 0 remainder 1 → bring down 0 gives 10 ÷ 9 = 1 remainder 1, and the remainder repeats, so the digits repeat 1.
- Algebra: let x = 0.111... then 10x = 1.111..., so 10x − x = 1 ⇒ 9x = 1 ⇒ x = 1/9.