To find the exact product of \(132.4 \times 27.9\), we can perform the multiplication:
\[ 132.4 \times 27.9 = 3,692.76 \]
Now we can evaluate Mario's estimates:
- Using compatible numbers: \(130 \times 30 = 3,900\)
- Rounding to the nearest whole number: \(132 \times 28 = 3,696\)
Next, let's compare the estimates to the exact product \(3,692.76\):
- The estimate using compatible numbers \(3,900\) is farther from \(3,692.76\) than the rounded estimate \(3,696\).
- The rounded estimate \(3,696\) is only \(3.24\) away from the exact product, while the compatible number estimate \(3,900\) is \(207.24\) away.
Now, evaluating the options given:
-
Using compatible numbers gave an answer closer to the exact answer.
- Incorrect. The rounded estimate is closer.
-
Rounding to the nearest whole number gave an answer closer to the exact answer.
- Correct. \(3,696\) is closer to \(3,692.76\) than \(3,900\).
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Both methods gave a reasonable estimate for the exact answer.
- Correct. Both estimates are in the vicinity of the exact answer, even though one is more accurate than the other.
-
Mario made errors in both estimates, so neither is reasonable.
- Incorrect. While both estimates are not exact, they are both reasonable approximations of the product.
Given this analysis, the correct statements about Mario's estimates are:
- Rounding to the nearest whole number gave an answer closer to the exact answer.
- Both methods gave a reasonable estimate for the exact answer.
2 answers