Use long division to convert 7/11 to a decimal a squiggly lines 1.571428 B squiggly lines 0.63 C 63 d 7.11

Answer 1

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

1. Set up the long division: Divide 7 by 11.

2. Initial Division:

   • 11 goes into 7, 0 times.
   • Place a decimal point and add a zero, making it 70.

3. Next Division:

   • 11 goes into 70, 6 times (since \( 11 \times 6 = 66 \)).
   • Write down 6 after the decimal point.
   • Subtract 66 from 70; you get 4.

4. Bring down a zero:

   • Now you have 40.
   • 11 goes into 40, 3 times (since \( 11 \times 3 = 33 \)).
   • Write down 3.
   • Subtract 33 from 40; you get 7.

5. Bring down another zero:

   • Now you have 70 again.
   • 11 goes into 70, 6 times.
   • Subtract 66 from 70; you get 4.

6. Continue the process:

   • Bring down a zero to make it 40.
   • 11 goes into 40, 3 times.
   • Subtract 33 from 40; you get 7.

You will notice that the process is repeating. The decimal continues as \( 0.636363 \ldots \), which we can represent as \( 0.63\overline{63} \).

Thus, the decimal representation of \( \frac{7}{11} \) is \( 0.636363...\).

Now, looking at the answer options:

• A: ~1.571428
• B: ~0.63 (using the notation for repeating decimals, we could write it as \( 0.63\overline{63} \))
• C: 63
• D: 7.11

The correct choice is B (0.63 with squiggly lines indicating the repeating part).