Use long division to convert 7/11 to a decimal.

Answer 1

To convert \( \frac{7}{11} \) to a decimal using long division, follow these steps:

1. Set up the long division, with 7 as the dividend and 11 as the divisor.

2. Since 7 is less than 11, you will add a decimal point and zeros to continue the division. Start with 7.0 (which is \( 7.000 \)).

3. Divide 11 into 70 (the first two digits). 11 goes into 70 six times (since \( 11 \times 6 = 66 \)). Write down 6 after the decimal point.

4. Subtract \( 66 \) from \( 70 \): \[ 70 - 66 = 4 \]

5. Bring down the next 0 to make it 40.

6. Divide 11 into 40. 11 goes into 40 three times (since \( 11 \times 3 = 33 \)). Write down 3 in the next decimal place.

7. Subtract \( 33 \) from \( 40 \): \[ 40 - 33 = 7 \]

8. Bring down the next 0 to again make it 70.

9. Repeat the process: Divide 70 by 11, which gives 6 again. Write down 6.

10. Subtract \( 66 \) from \( 70 \): \[ 70 - 66 = 4 \]

11. Bring down the next 0 to make it 40 again.

12. Divide 40 by 11, which gives 3 again.

13. Subtract \( 33 \) from \( 40 \): \[ 40 - 33 = 7 \]

At this point, you can see a pattern forming: the digits "63" are repeating. Therefore, the decimal representation of \( \frac{7}{11} \) is: \[ 0.\overline{63} \]

Thus, \( \frac{7}{11} = 0.636363...\) where "63" repeats indefinitely.