rounded error

简明释义

凑整误差

英英释义

例句

1.The final result was affected by a significant rounded error.

最终结果受到显著的四舍五入误差影响。

2.When calculating the budget, we need to account for any rounded error.

在计算预算时，我们需要考虑任何的四舍五入误差。

3.The rounded error can sometimes be larger than the actual error in the calculation.

有时，四舍五入误差可能比计算中的实际误差更大。

4.The rounded error in our measurements led to inaccurate results.

我们测量中的四舍五入误差导致了不准确的结果。

5.To minimize the rounded error, we should use more precise instruments.

为了最小化四舍五入误差，我们应该使用更精确的仪器。

作文

In the world of mathematics and data analysis, precision is key. However, when dealing with real-world applications, it is often necessary to simplify numbers for ease of understanding and communication. This is where the concept of rounded error comes into play. The term rounded error refers to the difference between a rounded number and the actual value. It is an important aspect to consider in various fields such as engineering, finance, and scientific research, where accurate measurements are crucial but rounding is frequently employed for simplicity.For instance, when a scientist measures the weight of a substance, the exact value might be 12.345 grams. However, for reporting purposes, they might round this number to 12.3 grams. The rounded error here would be the difference between 12.345 and 12.3, which equals 0.045 grams. While this may seem like a small discrepancy, in large-scale experiments or calculations, even minor errors can accumulate, leading to significant impacts on the results.In finance, rounding errors can also have profound implications. Consider a scenario where a company needs to calculate its total revenue from sales. If the individual sales figures are rounded to the nearest dollar, the final total could be slightly off due to rounded error. For example, if three products are sold for $10.49, $15.99, and $20.01, rounding these to $10, $16, and $20 respectively results in a total of $46. However, the actual total without rounding is $46.49, leading to a rounded error of $0.49. Over time, these small discrepancies can lead to misinformed business decisions.In engineering, the implications of rounded error can be even more critical. When designing a structure, engineers must ensure that all measurements are precise. If a measurement is rounded improperly, it could lead to structural failures or safety hazards. For example, if the load-bearing capacity of a beam is rounded down, it may not support the intended weight, resulting in catastrophic consequences. Therefore, engineers must be vigilant about tracking rounded error and ensuring that their designs account for potential inaccuracies.Moreover, in the realm of technology and programming, rounded error can affect algorithms and software performance. When dealing with floating-point arithmetic, computers often encounter rounding issues that can lead to unexpected behavior in programs. Developers must implement strategies to minimize rounded error, such as using higher precision data types or applying specific algorithms designed to reduce rounding discrepancies.In conclusion, while rounding is a common practice that aids in simplifying complex information, it is essential to understand the implications of rounded error. Whether in science, finance, engineering, or technology, being aware of how rounding affects accuracy can help professionals make better decisions and avoid potential pitfalls. As we navigate a world filled with data, recognizing the significance of rounded error will enable us to approach problems with a clearer perspective and a greater appreciation for precision in our work.

在数学和数据分析的世界中，精确性是关键。然而，在处理现实应用时，通常有必要简化数字，以便于理解和交流。这就是rounded error（舍入误差）概念的出现。术语rounded error指的是一个舍入数字与实际值之间的差异。它在工程、金融和科学研究等各个领域都很重要，因为这些领域需要准确的测量，但经常为了简单而进行舍入。例如，当科学家测量某种物质的重量时，确切的值可能是12.345克。然而，为了报告，他们可能将这个数字舍入为12.3克。这里的rounded error就是12.345和12.3之间的差异，等于0.045克。虽然这看起来是一个小的差异，但在大规模实验或计算中，即使是微小的误差也会累积，从而对结果产生重大影响。在金融领域，舍入误差也可能有深远的影响。考虑这样一个场景：一家公司需要计算其销售总收入。如果单个销售数字被舍入到最接近的美元，最终总数可能由于rounded error而略有偏差。例如，如果三种产品的售价分别为$10.49、$15.99和$20.01，将这些价格舍入为$10、$16和$20，最终总额为$46。然而，不舍入的实际总额为$46.49，导致rounded error为$0.49。随着时间的推移，这些小的差异可能导致错误的商业决策。在工程学中，rounded error的影响可能更为关键。在设计结构时，工程师必须确保所有测量都是精确的。如果测量不当舍入，可能导致结构失效或安全隐患。例如，如果一根梁的承载能力被向下舍入，可能无法支撑预期的重量，导致灾难性的后果。因此，工程师必须警惕追踪rounded error，并确保他们的设计考虑潜在的不准确性。此外，在技术和编程领域，rounded error可能会影响算法和软件性能。在处理浮点算术时，计算机经常遇到舍入问题，这可能导致程序意外行为。开发人员必须实施策略以最小化rounded error，例如使用更高精度的数据类型或应用专门设计用于减少舍入差异的特定算法。总之，虽然舍入是一种常见的做法，有助于简化复杂信息，但理解rounded error的影响至关重要。无论是在科学、金融、工程还是技术领域，了解舍入如何影响准确性可以帮助专业人士做出更好的决策，避免潜在的陷阱。当我们在充满数据的世界中导航时，认识到rounded error的重要性将使我们能够以更清晰的视角和更大的精确性来处理问题。