To convert \( \frac{7}{11} \) to a decimal using long division, we follow these steps:
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Set up the division: We are dividing 7 by 11, which is \( 7 \div 11 \).
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Since 11 does not go into 7, we will place a decimal point and add a zero, treating it as \( 70 \).
- Now, we have \( 11 \) into \( 70 \).
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Determine how many times 11 fits into 70:
- \( 11 \) goes into \( 70 \) six times (because \( 11 \times 6 = 66 \)).
- Subtract \( 66 \) from \( 70 \) to get \( 4 \).
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Bring down another zero making it \( 40 \).
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Now divide again:
- \( 11 \) goes into \( 40 \) three times (because \( 11 \times 3 = 33 \)).
- Subtract \( 33 \) from \( 40 \) to get \( 7 \).
-
Bring down another zero making it \( 70 \) again.
-
Repeat the process:
- \( 11 \) goes into \( 70 \) six times again (because \( 11 \times 6 = 66 \)).
- Subtract \( 66 \) from \( 70 \) to get \( 4 \).
- Bring down another zero, making it \( 40 \).
- \( 11 \) goes into \( 40 \) three times again (because \( 11 \times 3 = 33 \)).
- Subtract \( 33 \) from \( 40 \) to get \( 7 \) again.
The decimals will continue to repeat with the pattern: \( 0.636363...\).
Putting this all together, we find that:
\[
\frac{7}{11} \approx 0.636363...
\]
However, the equivalent decimal can also be expressed as \( \approx 0.636 \) when rounded or noted for its repeating nature.
In this case, among the options provided, the closest response that reflects a decimal representation is:
≈0.63 (approximately equals 0.63).