To convert the mixed number \( 6 \frac{7}{15} \) to a decimal, we can follow these steps:
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Separate the whole number and the fraction: The whole number part is \( 6 \) and the fractional part is \( \frac{7}{15} \).
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Convert the fraction \( \frac{7}{15} \) to a decimal using long division:
- Divide \( 7 \) by \( 15 \).
- Set it up: \( 7.000000 \div 15 \)
\[ 15 ) 7.000000 \]
- 15 goes into 70: \( 4 \) times (since \( 15 \times 4 = 60 \)).
- Write \( 4 \) above the line.
- Subtract \( 60 \) from \( 70 \), leaving \( 10 \).
- Bring down a \( 0 \) to make \( 100 \).
\[ 15) 70.000000 \quad - 60 \quad \quad 10 \]
- 15 goes into 100: \( 6 \) times (since \( 15 \times 6 = 90 \)).
- Write \( 6 \) next to \( 4 \) above the line.
- Subtract \( 90 \) from \( 100 \), leaving \( 10 \).
- Bring down another \( 0 \) to make \( 100 \) again.
\[ 15) 70.000000 \quad - 60 \quad \quad 10 \quad - 90 \quad \quad 10 \]
- This process will continue to repeat (as shown, we'll keep getting \( 10 \) when bringing down a \( 0 \)). Thus the division yields:
\[ 0.4666\ldots \]
This means \( \frac{7}{15} \approx 0.4667 \) (rounded to four decimal places).
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Combine with the whole number: Now add the whole number part to the decimal from the fraction:
\[ 6 + 0.4667 = 6.4667 \]
Thus, the decimal equivalent of \( 6 \frac{7}{15} \) is approximately \( \boxed{6.4667} \).
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