Use long division to convert 7/11 to a decimal. (1 point)
A. ~1.571428
B. 63
C. 7.11
D. ~0.63
The long division to convert 7/11 to a decimal is as follows:
0.636363...
By continuing the pattern of 36 repeating, the decimal representation of 7/11 is approximately 0.636363...
Therefore, the correct option is D. ~0.63.
To convert 7/11 to a decimal using long division, follow these steps:
Step 1: Set up the division.
_____0. |
11 | 7
Step 2: Divide the first digit of the dividend by the divisor.
The first digit of the dividend is 7. Since 11 cannot go into 7, we bring down the next digit, which is 0.
_____0. |
11 | 70
Step 3: Divide the first two digits of the dividend by the divisor.
Now, we have 70 as the new dividend. Dividing 70 by 11 gives 6.
_____0. |
11 | 70
-66
___
4
Step 4: Bring down the next digit and repeat the process.
We bring down the next digit, which is 0. After dividing 40 by 11, we get 3 as the quotient.
_____0. |
11 | 700
-66
___
40
-33
___
70
Step 5: Continue repeating the process until you reach the desired level of precision or the remainder is 0.
Bringing down the next digit, which is also 0, and dividing 700 by 11 gives 63. Now our remainder is 0.
_____0. |
11 | 700
-66
___
40
-33
___
70
-66
___
40
-33
___
70
-66
__
40
-33
__
7
Step 6: Write the final decimal.
Since the remainder is 7, we write the final decimal as 0.636363...
Therefore, the correct answer is D. ~0.63.
To convert a fraction to a decimal using long division, follow these steps:
Step 1: Write down the fraction as a division problem.
In this case, the fraction is 7/11, so we write it as 7 ÷ 11.
Step 2: Perform the long division.
Start by dividing 7 by 11. The quotient is the whole number part of the decimal, and the remainder will be used to find the fractional part.
0.6 3 (quotient)
______
11 ) 7.0 0 (dividend)
In the above equation, the division starts with 7 divided by 11, which gives a quotient of 0. We then bring down a zero and divide 70 by 11, which gives a quotient of 6. The decimal part is 0.6.
Step 3: Determine the fractional part.
The remainder in the division becomes the numerator of the fraction, and the divisor becomes the denominator. In this case, the remainder is 4. So, the fractional part is 4/11.
Step 4: Combine the whole number part and the fractional part.
Combining the whole number part (0) and the fractional part (4/11), we get 0.6 + 4/11 as the decimal equivalent.
Step 5: Simplify the fraction if necessary.
To simplify the fraction 4/11, we find that it is already simplified.
So, the decimal equivalent of 7/11 is approximately 0.6 + 4/11.
To find the decimal value, you can either perform the addition or use a calculator.
0.6 + 4/11 ≈ 0.6 + 0.363 (rounded to three decimal places) ≈ 0.963.
Therefore, the correct answer is D. ~0.63, which is approximately 0.963 when rounded to two decimal places.