To find \(-492.89 - (-871.78)\), we can use the property of the additive inverse. When subtracting a negative number, it's equivalent to adding its positive counterpart.
Thus,
\[ -492.89 - (-871.78) = -492.89 + 871.78 \]
Now, we can perform the addition:
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Add the absolute values: \[ 871.78 - 492.89 \]
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Align the numbers for addition: \[ \begin{array}{r} 871.78 \ -492.89 \ \hline \end{array} \]
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Subtract the values:
- Start from the rightmost digit:
- \(8 - 9\): we need to borrow, making it 18 - 9 = 9 (we borrow 1 from 7, changing it to 6)
- \(6 - 8 = -2\), so we borrow again, making it 16 - 8 = 8 (now 6 becomes 5)
- \(5 - 2 = 3\)
- Now we have \(8 - 4 = 4\)
- Lastly, \(8 - 0 = 8\)
- Start from the rightmost digit:
So,
\[ 871.78 - 492.89 = 378.89 \]
Therefore,
\[ -492.89 - (-871.78) = 378.89 \]
The final result is:
\[ \boxed{378.89} \]