Question

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

Answer 1

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

1. **Set up the division:** Write 2.000 (to allow for decimal places) and divide by 9.
2. **Perform the long division:**
- 9 goes into 2: 0 times.
- Place a decimal point and add a zero (making it 20).
- 9 goes into 20: 2 times (as \( 9 \times 2 = 18 \)).
- Subtract 18 from 20, leaving a remainder of 2.
- Bring down the next 0 (making it 20 again).
- Repeat: 9 goes into 20: 2 times (again, \( 9 \times 2 = 18 \)).
- Subtract 18 from 20, leaving 2.
- Bring down another 0 (still making it 20).

This process will repeat indefinitely, indicating that \( \frac{2}{9} = 0.222... \)

3. **Round the decimal:** To get one decimal place, we look at the first digit after the decimal point, which is 2. The next digit is also 2, which means we round down.

Thus, \( \frac{2}{9} \) rounded to one decimal place is \( 0.2 \).