Use long division to convert 7/11 to a decimal.(1 point)
Responses
7.11
7.11
≈1.571428
63
63
≈0.63
The correct response is 0.63
To convert the fraction 7/11 into a decimal using long division, follow these steps:
1. Set up the division problem with 7 as the dividend and 11 as the divisor:
- Place the dividend (7) inside the long division symbol (÷).
- Write the divisor (11) outside the division symbol.
_______
11 | 7
2. Divide the first digit of the dividend (7) by the divisor (11):
- 7 ÷ 11 = 0 (since 11 is not a factor of 7).
3. Place a decimal point above the division bar, directly above the decimal point in the dividend:
_______
11 | 7 . 0
4. Add a zero after the decimal point and bring it down next to the next digit of the dividend (0).
_______
11 | 7 . 0
- 6
5. Divide the new dividend (60) by the divisor (11):
- 60 ÷ 11 = 5 (since 11 goes into 60 five times).
6. Write the result (5) above the division bar, to the right of the previous quotient digit (0).
_______
11 | 7 . 0
- 6
5
7. Subtract the product of the new quotient digit (5) and the divisor (11) from the previous dividend (60). Write the difference (10) below the line.
_______
11 | 7 . 0
- 6
5
-55
8. Bring down the next digit of the dividend (7) next to the difference (10):
_______
11 | 7 . 0
- 6
5
-55
7
9. Divide the new dividend (75) by the divisor (11):
- 75 ÷ 11 = 6 (since 11 goes into 75 six times).
10. Write the result (6) above the division bar, to the right of the previous quotient digits (0 and 5).
_______
11 | 7 . 0
- 6
5
-55
66
11. Subtract the product of the new quotient digit (6) and the divisor (11) from the previous dividend (75). Write the difference (9) below the line.
_______
11 | 7 . 0
- 6
5
-55
66
-66
9
12. Bring down the next digit of the dividend (0) next to the difference (9):
_______
11 | 7 . 0
- 6
5
-55
66
-66
90
13. Divide the new dividend (90) by the divisor (11):
- 90 ÷ 11 = 8 (since 11 goes into 90 eight times).
14. Write the result (8) above the division bar, to the right of the previous quotient digits (0, 5, and 6).
_______
11 | 7 . 0
- 6
5
-55
66
-66
90
88
15. Subtract the product of the new quotient digit (8) and the divisor (11) from the previous dividend (90). Write the difference (2) below the line.
_______
11 | 7 . 0
- 6
5
-55
66
-66
90
88
-88
2
16. Bring down any remaining digits of the dividend (0) next to the difference (2):
_______
11 | 7 . 0
- 6
5
-55
66
-66
90
88
-88
20
17. Divide the new dividend (20) by the divisor (11):
- 20 ÷ 11 ≈ 1.818181 (since the division doesn't terminate).
18. Continue the long division process until you reach the desired level of precision.
Putting it all together, 7/11 can be approximated as 0.63 (rounded to two decimal places).
To convert the fraction 7/11 to a decimal using long division, you need to divide 7 by 11. Here are the steps:
1. Write down 7 as the numerator and 11 as the denominator.
7
--
11
2. Start dividing: How many times does 11 go into 7? Since 11 is larger than 7, we can't divide the whole number. So, we add a decimal point and a zero after 7 and bring it down.
0. (quotient placeholder)
7 0
--
11
3. How many times does 11 go into 70? Divide 70 by 11 to get the quotient.
0.6 (quotient gets updated)
7 0
--
11
4. Multiply the quotient (0.6) by 11 and subtract it from 70 to find the remainder.
0.6
x 11
-----
66.0 (subtract this from 70)
-66.0
------
4.0
5. Bring down the next digit of the dividend, which is 0. We can add a zero after the decimal point and continue dividing.
0.63 (quotient gets updated)
7 0.0
----
11
6. How many times does 11 go into 40? Divide 40 by 11 to get the quotient.
0.63
7 0.0
----
11
7. Multiply the quotient (0.63) by 11 and subtract it from 40 to find the remainder.
0.63
x 11
-----
6.93 (subtract this from 70.0)
-6.93
-----
3.07
8. Bring down the next digit of the dividend, which is 7. We can add another zero after the decimal point and continue dividing.
0.636 (quotient gets updated)
7 0.07
-----
11
9. Since we have a repeating pattern of 63, we can see that the decimal value of 7/11 is approximately 0.636363...
Therefore, the decimal equivalent of 7/11 is approximately 0.636 or 0.63 rounded to two decimal places.