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Evaluate: 271 .8 div 15...

Evaluate:
`271 .8 div 15`

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To evaluate \( 271.8 \div 15 \), we will follow the steps of long division while keeping track of the decimal point. ### Step-by-Step Solution: 1. **Set up the division**: Write 271.8 as the dividend (inside the division bracket) and 15 as the divisor (outside the division bracket). \[ \begin{array}{r|l} 15 & 271.8 \\ \end{array} \] 2. **Divide the first part**: Look at the first two digits of 271, which is 27. Determine how many times 15 can go into 27. - 15 goes into 27 once (1 time). - Multiply: \( 15 \times 1 = 15 \). - Subtract: \( 27 - 15 = 12 \). \[ \begin{array}{r|l} 15 & 271.8 \\ & -15 \\ \hline & 12 \\ \end{array} \] 3. **Bring down the next digit**: Bring down the next digit (1 from 271.8) to make it 121. \[ \begin{array}{r|l} 15 & 271.8 \\ & -15 \\ \hline & 121 \\ \end{array} \] 4. **Divide 121 by 15**: Determine how many times 15 can go into 121. - 15 goes into 121 eight times (8 times). - Multiply: \( 15 \times 8 = 120 \). - Subtract: \( 121 - 120 = 1 \). \[ \begin{array}{r|l} 15 & 271.8 \\ & -15 \\ \hline & 121 \\ & -120 \\ \hline & 1 \\ \end{array} \] 5. **Bring down the next digit**: Bring down the next digit (8 from 271.8) to make it 18. \[ \begin{array}{r|l} 15 & 271.8 \\ & -15 \\ \hline & 121 \\ & -120 \\ \hline & 18 \\ \end{array} \] 6. **Divide 18 by 15**: Determine how many times 15 can go into 18. - 15 goes into 18 once (1 time). - Multiply: \( 15 \times 1 = 15 \). - Subtract: \( 18 - 15 = 3 \). \[ \begin{array}{r|l} 15 & 271.8 \\ & -15 \\ \hline & 121 \\ & -120 \\ \hline & 18 \\ & -15 \\ \hline & 3 \\ \end{array} \] 7. **Add a decimal point**: Since we have reached the decimal in 271.8, we place a decimal point in the quotient above the decimal point in the dividend. 8. **Bring down a zero**: Add a zero to the remainder 3 to make it 30. \[ \begin{array}{r|l} 15 & 271.8 \\ & -15 \\ \hline & 121 \\ & -120 \\ \hline & 18. \\ & -15 \\ \hline & 30 \\ \end{array} \] 9. **Divide 30 by 15**: Determine how many times 15 can go into 30. - 15 goes into 30 two times (2 times). - Multiply: \( 15 \times 2 = 30 \). - Subtract: \( 30 - 30 = 0 \). \[ \begin{array}{r|l} 15 & 271.8 \\ & -15 \\ \hline & 121 \\ & -120 \\ \hline & 18. \\ & -15 \\ \hline & 30 \\ & -30 \\ \hline & 0 \\ \end{array} \] 10. **Final result**: Since there is no remainder, the final answer is \( 18.12 \). ### Answer: \[ 271.8 \div 15 = 18.12 \]
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