To understand Lucita's mistake, let's first analyze the division problem \(3.302 \div -1.27\).
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If we ignore the negative sign and simply consider \(3.302 \div 1.27\):
- To get an estimate, we can round \(3.302\) to \(3.3\) and \(1.27\) to \(1.3\).
- Then we can estimate \(3.3 \div 1.3\).
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To make this division easier, we can convert these numbers into fractions:
- \(3.3 \div 1.3\) is similar to \(\frac{33}{10} \div \frac{13}{10} = \frac{33}{13}\).
- A rough estimate for \(\frac{33}{13}\) is approximately \(2.54\) (because \(13\) goes into \(33\) about \(2.5\) times).
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Now accounting for the sign, since we are dividing a positive number by a negative number, the result would be negative. Thus, our estimated result should be around \(-2.54\).
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Lucita, however, estimated the result to be \(-3\). This estimate of \(-3\) is too low compared to the actual result.
Considering her actual result of \(-0.026\), which is much smaller in magnitude than her estimate of \(-3\), it suggests that she misunderstood the scale of the numbers involved in the division.
So, the correct assessment of her mistake is that Lucita's estimate is too low.