2/9 as a Decimal and Percentage (0.2̅ and 22.22%)
Updated · By the SolverCalc team
Quick answer
2/9 = 0.2222… (written 0.2̅) ≈ 22.22%.
Students often search for “2 9 as a decimal” when a worksheet asks them to convert two ninths. The result is a repeating decimal: the digit 2 continues forever. Here is how to find it, how to write it correctly and how to turn it into a percentage.
Converting 2/9 to a decimal
- Set up the division 2 ÷ 9. Because 9 does not fit into 2, write 0 and a decimal point.
- Bring down a zero: 20 ÷ 9 = 2 remainder 2.
- Bring down another zero: 20 ÷ 9 = 2 remainder 2 again.
- The remainder is always 2, so the digit 2 repeats forever: 0.2222…
In math class this is written with a bar over the repeating digit: 0.2̅. On a calculator display you will see 0.2222222222 because the screen can only show a limited number of digits.
Converting 2/9 to a percentage
- Start with the decimal: 0.2222…
- Multiply by 100: 22.222…
- Round to two decimal places: 22.22%. Exactly, 2/9 = 22 2⁄9 %.
The pattern for all ninths
| Fraction | Decimal | Percentage (rounded) |
|---|---|---|
| 1/9 | 0.1111… | 11.11% |
| 2/9 | 0.2222… | 22.22% |
| 4/9 | 0.4444… | 44.44% |
| 5/9 | 0.5555… | 55.56% |
| 7/9 | 0.7777… | 77.78% |
Any fraction with 9 in the denominator (and a numerator from 1 to 8) produces the numerator as a repeating digit. That makes ninths easy to remember once you see the pattern.
Common mistakes
- Writing 2/9 as 0.29 by placing the digits after a decimal point.
- Rounding 0.2222… to 0.23 instead of 0.22 (the next digit is 2, so you round down).
- Forgetting the bar notation when an exact answer is required.
Turning 0.2̅ back into 2/9
A neat algebra trick proves the answer. Let x = 0.2222… Multiply both sides by 10 to get 10x = 2.2222… Now subtract the first equation from the second: 10x − x = 2.2222… − 0.2222…, which leaves 9x = 2. Dividing by 9 gives x = 2/9. The endless tail of 2s cancels out, which is exactly why the repeating decimal and the fraction are equal.