Use long division to convert 7/11 to a decimal.(1 point)

Question

Responses

≈0.63
approximately equals 0.63

≈1.571428
approximately equals 1.571428

63
63

7.11

Answer 1

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

1. Set up the division: We are dividing 7 by 11.

     0.636363...
   _______________
   11 | 7.000000
   

2. Divide 7 by 11: Since 7 is less than 11, we start with 0. Add a decimal point and a zero to make it 70.

3. Divide 70 by 11: 11 goes into 70 six times (since \( 11 \times 6 = 66 \)).

     0.6
   _______________
   11 | 70.000
       - 66
       _____
         4
   

4. Bring down a zero to make 40.

5. Divide 40 by 11: 11 goes into 40 three times (since \( 11 \times 3 = 33 \)).

     0.63
   _______________
   11 | 70.000
       - 66
       _____
         40
       - 33
       _____
          7
   

6. Bring down another zero to make 70 again.

7. Repeat the process: We see that we are back at 70, so the cycle will continue:

     0.636363...
   

From this division, we see that the decimal repeats. Therefore, \( \frac{7}{11} \) can be expressed as:

\[ 0.\overline{63} \]

The answer closest to this in your options would be:

≈0.63 (approximately equals 0.63).