Use long division she convert 7/11 to a decimal
To convert the fraction 7/11 to a decimal, we will perform long division.
First, we write the fraction as a division problem: 7 รท 11.
0.6
__________
11 ) 7.0
Starting with the tenths place, we divide 11 into 70. Since 11 can be divided by 70 exactly 6 times, we write 6 as the quotient above the division line and multiply it by 11, which equals 66. We then subtract 66 from 70, which gives us a remainder of 4.
0.6
__________
11 ) 7.0
6.6
-----
0.4
To continue the division, we bring down the 0 from the decimal part and divide 11 into 40. This time, 11 can be divided by 40 exactly 3 times, so we write 3 as the next digit of our quotient and multiply it by 11, which equals 33. We subtract 33 from 40, giving us a remainder of 7.
0.6
__________
11 ) 7.0
6.6
-----
0.40
0.33
-----
7
Since the remainder is not zero and there are no more digits to bring down, we can conclude that the decimal representation of 7/11 is 0.63 (rounded to two decimal places).
Sure! We can use long division to convert the fraction 7/11 into a decimal.
Step 1: Write down the fraction 7/11.
Step 2: Set up the long division problem by dividing 7 by 11.
_____
11 | 7
Step 3: Notice that 11 does not evenly divide into 7. In this case, we need to add a decimal point to the quotient to convert it to a decimal.
Step 4: Bring down a zero and place it after the decimal point above the division bar.
_____
11 | 7.0
Step 5: Divide 7 by 11. The quotient is 0.63 (rounded to two decimal places).
_____
11 | 7.0
- 0
70
------
40
Step 6: Bring down the next zero and place it after the 40.
_____
11 | 7.00
- 0
70
------
40
- 33
--------
70
Step 7: Divide 70 by 11. The quotient is 6.36 (rounded to two decimal places).
_____
11 | 7.00
- 0
70
------
40
- 33
--------
70
- 66
--------
40
Step 8: Bring down another zero after the 40.
_____
11 | 7.000
- 0
70
------
40
- 33
--------
70
- 66
--------
40
- 33
--------
70
Step 9: Divide 70 by 11. The quotient is 6.363 (rounded to three decimal places).
Continue this process if you want to find more decimal places, but for this fraction, 7/11 is approximately equal to 0.636 (rounded to three decimal places).
To convert a fraction to a decimal using long division, follow these steps:
1. Set up the long division: Write the numerator of the fraction (7) inside the division bracket and the denominator (11) outside the bracket.
_____
11 | 7
2. Divide: Consider how many times 11 can go into 7. Since 11 is larger than 7, we need to add a decimal point to the right of 7 and add a zero after the decimal point:
_____
11 | 7.0
3. Bring down the zero: Now, bring down the next digit (which is a zero) after the decimal point:
_____
11 | 7.0
-
4. Perform the division: Look for the largest multiple of 11 that is less than or equal to 70. In this case, 11 multiplied by 6 is 66, which is the largest multiple of 11 less than 70. So, write the number 6 above the division bracket.
_6___
11 | 7.0
-
5. Subtract: Subtract 66 (6 times 11) from 70:
_6___
11 | 7.0
- 66
-----
4.0
6. Bring down the next digit: Bring down the next digit (which is another zero) after the decimal point:
_6___
11 | 7.00
- 66
-----
40
7. Multiply and subtract: Determine how many times 11 can be multiplied by to get a value less than or equal to 40. In this case, it is 3 (3 x 11 = 33). Write 3 above the division bracket. Then, subtract 33 from 40:
_63__
11 | 7.00
- 66
-----
40
- 33
-----
70
8. Bring down the next zero: Bring down another zero after the decimal point:
_63__
11 | 7.000
- 66
-----
40
- 33
-----
70
9. Repeat the process: Multiply and subtract until you obtain the desired level of decimal precision or until the division process completes. In this case, the pattern repeats, as we already encountered a remainder of 70:
_63__ (repeating pattern)
11 | 7.0000
- 66
-----
40
- 33
-----
70
- 66
-----
40
- 33
-----
70
- 66
-----
40
Since we have reached the repeating pattern, we can conclude that 7/11 as a decimal is approximately 0.636363...