To convert \( \frac{7}{11} \) to a decimal using long division, follow these steps:
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Set up the long division: Divide 7 by 11. Since 7 is less than 11, we start with 0.
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Add a decimal point: We can add a decimal point and zeros to continue the division. So, we consider it as \( 7.000 \).
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Divide:
- 11 goes into 70 (which is 7.0 with one zero added) six times: \( 11 \times 6 = 66 \).
- Write 6 above the division line. Subtract: \( 70 - 66 = 4 \).
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Bring down the next 0: Now we have 40.
- 11 goes into 40 three times: \( 11 \times 3 = 33 \).
- Write 3 above the division line. Subtract: \( 40 - 33 = 7 \).
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Repeat: Bring down another 0, giving us 70 again. Repeat the same steps:
- 11 goes into 70 six times (66), leaving us with 4.
- Bring down another 0 to get 40 again.
- 11 goes into 40 three times (33), leaving 7.
The process will keep repeating in the cycle of 6 and 3.
So, the decimal representation of \( \frac{7}{11} \) is:
\[ 0.\overline{63} \]
Since none of the options exactly match this conclusion in notation, the best response approximating \( \frac{7}{11} \) in decimal form would be:
≈0.63
This translates to "approximately equals 0.63".