To convert the rational number 2716 into a decimal using long division, we proceed as follows:
- Identify the number you want to convert (let's write it as a fraction: \( \frac{2716}{1000} \), since you want to express it in decimal form).
- Next, we perform long division of 2716 by 1000.
To do this:
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Divide 2716 by 1000.
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Since 1000 goes into 2716 two times, we write down 2.
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Then, multiply 2 by 1000 (which is 2000) and subtract it from 2716:
\( 2716 - 2000 = 716 \)
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Now, bring down two zeros to the 716 (to handle the decimal): \( 71600 \).
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Divide 71600 by 1000. 1000 goes into 71600 seventy-one times, so you write down 7.
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Multiply 7 by 1000 (which is 7000) and subtract:
\( 71600 - 7000 = 1600 \)
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Bring down two more zeros (to keep going with the decimal): \( 160000 \).
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Divide 160000 by 1000. 1000 goes into 160000 one hundred sixty times, so you write down 6.
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Multiply 6 by 1000 (which is 6000) and subtract:
\( 16000 - 6000 = 1000 \)
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Finally, bring down two more zeros again: \( 10000 \).
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Divide 10000 by 1000. 1000 goes into 10000 ten times, so you write down 10.
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Multiply 10 by 1000, which gives you exactly 10000, so:
\( 10000 - 10000 = 0 \)
At this point, we have our answer.
Thus, the decimal representation of 2716 is:
\[ 2.4375 \]
So, your answer is correct, \( 2.4375 \).
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