- Perform an estimation for each calculation to check if the result is reasonable.
- Expression 1: \(46.4 \times 34.25 \approx 1564\), consistent with \(1589.2\).
- Expression 2: \(195.3 \times 0.724 \approx 140\), inconsistent with \(14.1\).
- Expression 3: \((41.25 \times 6.8) + 35.3 \approx 322\), consistent with \(315.8\).
- Expression 4: \((204 + 98) \times 8.3 \approx 2400\), inconsistent with \(250.7\).
- Conclusion: The definitely wrong calculations are \(\boxed{2 \text{ and } 4}\).
Explanation
- Analyzing and Estimating the Calculations
To determine which of the four provided calculations are incorrect, we perform an estimation for each one to check their order of magnitude.
1) \(46.4 \times 34.25\): We can estimate this as \(46 \times 34 \approx 1564\). Since the provided answer is \(1589.2\), which is very close to our estimate, this calculation appears to be correct.
2) \(195.3 \times 0.724\): We can estimate this as \(200 \times 0.7 = 140\). The provided answer is \(14.1\). Because \(14.1\) is significantly smaller than our estimate of \(140\), this calculation is incorrect.
3) \((41.25 \times 6.8) + 35.3\): We can estimate this as \((41 \times 7) + 35 = 287 + 35 = 322\). The provided answer is \(315.8\), which is close to our estimate, so this calculation is correct.
4) \((204 + 98) \times 8.3\): We can estimate this as \((200 + 100) \times 8 = 300 \times 8 = 2400\). The provided answer is \(250.7\). Because \(250.7\) is nowhere near our estimate of \(2400\), this calculation is clearly incorrect.
- Identifying the Incorrect Calculations
Comparing the results of our estimates to the provided answers, we find that:
- For calculation 2, our estimate of \(140\) differs greatly from the provided value of \(14.1\).
- For calculation 4, our estimate of \(2400\) differs greatly from the provided value of \(250.7\).
In both cases, the error likely stems from a mistake in the decimal place placement. Thus, calculations 2 and 4 are definitely wrong.
Examples
Estimation is a vital skill in daily life, such as when quickly checking if a bill, a grocery total, or a distance calculation makes sense. For instance, if you are buying 5 items that cost approximately \$20 each, you can estimate that your total should be around \$100. If the register displays a total of \$10, you immediately know there is a mistake. Similarly, if you are planning a trip and calculate that driving 300 miles at 60 miles per hour should take about 5 hours, but your GPS says it will take 50 hours, you recognize an error in the calculation. These quick mental checks save time and prevent errors in practical decision-making.