Question

Use long division to convert 2/9
to a decimal. Your approximation should have one decimal place.(1 point)

Answer 1

To convert the fraction \( \frac{2}{9} \) to a decimal using long division, we can divide 2 by 9.

1. **Set up the long division**:
- 2 is the dividend (the number being divided).
- 9 is the divisor (the number you are dividing by).
- Since 2 is less than 9, we write 2.0 and proceed with the division.

2. **Divide**:
- 9 goes into 20 two times (since \( 9 \times 2 = 18 \)).
- Write 2 above the line (in the decimal place).
- Subtract \( 18 \) from \( 20 \), which gives us \( 2 \).

3. **Bring down a 0**:
- Bring down another 0 making it 20 again.

4. **Repeat the process**:
- 9 goes into 20 two times again.
- Write another 2 above the line. Now you have \( 0.2 \) (from the first division).
- Subtract \( 18 \) from \( 20 \), giving you \( 2 \).

5. **Bring down another 0 (if necessary)**:
- You will repeat the cycle as bringing down another 0 gives you 20 again.

Continuing this process shows that \( \frac{2}{9} \) evaluates to \( 0.222...\) where the 2 recurs indefinitely.

Since you need the answer to one decimal place, the decimal approximation of \( \frac{2}{9} \) is:

\[
\boxed{0.2}
\]