To convert \( 6 \frac{7}{20} \) to a decimal, we can first convert it to an improper fraction and then perform long division.
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Convert \( 6 \frac{7}{20} \) to an improper fraction: \[ 6 \frac{7}{20} = \frac{6 \times 20 + 7}{20} = \frac{120 + 7}{20} = \frac{127}{20} \]
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Now divide 127 by 20 using long division:
- 20 goes into 127 six times since \( 20 \times 6 = 120 \).
- Subtract \( 120 \) from \( 127 \) which leaves a remainder of \( 7 \).
- This gives us \( 6 \) as the whole number part and we need to convert the decimal part next.
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Now, divide the remainder by 20:
- Take the remainder \( 7 \), and append a decimal point (consider it as \( 7.0 \)).
- \( 20 \) goes into \( 70 \) three times since \( 20 \times 3 = 60 \).
- Subtract \( 60 \) from \( 70\) which leaves a remainder of \( 10 \).
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Continue the division:
- Now divide \( 10 \) by \( 20 \) and append another zero.
- \( 20 \) goes into \( 100 \) five times since \( 20 \times 5 = 100 \).
- Subtract \( 100 \) from \( 100\) which leaves a remainder of \( 0 \).
Putting it all together, we have: \[ 6 + 0.35 = 6.35 \]
Thus, \( 6 \frac{7}{20} = 6.35 \).
Therefore, the correct answer is c) 6.35.