To convert \( 6 \frac{7}{20} \) to a decimal using long division, we first need to convert the fractional part \( \frac{7}{20} \) to a decimal.
- Set up the long division: We divide 7 by 20.
\[ 20 \text{ goes into } 7: 0 \text{ times} \] So we can write \( 7.000 \) for the long division to help in our calculation.
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Add decimal point: Place a decimal point in the quotient and in the dividend:
- 20 into 70 (since we shift the decimal and consider 7.0 as 70).
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Long division:
- \( 20 \) goes into \( 70 \) three times because \( 20 \times 3 = 60 \).
- Subtract \( 60 \) from \( 70 \): \( 70 - 60 = 10 \).
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Bring down the next digit (which is 0, making it 100):
- Now, ask how many times \( 20 \) goes into \( 100 \).
- \( 20 \) goes into \( 100 \) five times because \( 20 \times 5 = 100 \).
- Subtract \( 100 \) from \( 100 \): \( 100 - 100 = 0 \).
Now we have completed the division, finding that:
\[ \frac{7}{20} = 0.35 \]
Next, we add this result to the whole number part \( 6 \):
\[ 6 + 0.35 = 6.35 \]
Therefore, \( 6 \frac{7}{20} \) as a decimal is:
\[ \boxed{6.35} \]