Question

Use long division to convert 7/11 to a decimal

Answer 1

To convert 7/11 to a decimal using long division, follow these steps:

1. Place the dividend (7) inside the long division bracket, and the divisor (11) outside the bracket.
0.| 7
------
11|

2. Divide the first digit of the dividend (7) by the divisor (11). Write the quotient (0) above the long division bracket.

0.| 7
------
11|
0

3. Multiply the quotient (0) by the divisor (11) and write the result below the dividend, aligned with the first digit.

0.| 7
------
11| 0

4. Subtract the result from step 3 from the first digit of the dividend (7). Write the difference (7) below the subtraction line.

0.| 7
------
11| 0
-
7

5. Bring down the next digit (0) from the dividend and append it to the difference obtained in step 4.

0.| 7
------
11| 0
-
70

6. Divide the new dividend (70) by the divisor (11). Write the new quotient (6) above the long division bracket.

0.| 7
------
11| 0
-
70
-66

7. Multiply the quotient (6) by the divisor (11) and write the result (66) below the new dividend, aligned with the first digit.

0.| 7
------
11| 0
-
70
-66
--
4

8. Subtract the result from step 7 from the new dividend (70). Write the difference (4) below the subtraction line.

0.| 7
------
11| 0
-
70
-66
--
4

9. Since the dividend (4) is less than the divisor (11), we have obtained the complete decimal representation.
The decimal form of 7/11 is 0.636363... (where the digit 36 repeats indefinitely).