To convert \( \frac{2}{9} \) to a decimal using long division, we proceed as follows:
- Set up the long division by dividing 2 by 9. Since 2 is less than 9, we will write 0 and proceed with decimal places.
- Add a decimal point and a zero to 2, making it 20.
- Divide 20 by 9:
- 9 goes into 20 two times (because \( 9 \times 2 = 18 \)).
- Write down 2 as the first digit after the decimal point.
- Subtract 18 from 20, which gives us a remainder of 2.
- Bring down another 0 (making it 20 again) and repeat the process:
- 9 goes into 20 two times, just like before.
- Again, subtract 18 from 20 to get a remainder of 2.
- Since we are seeking just one decimal place, we can stop here.
After performing the long division, we find that:
\[ \frac{2}{9} \approx 0.2 \]
Thus, the approximation of \( \frac{2}{9} \) to one decimal place is \( 0.2 \).