limiting error

简明释义

极限误差

英英释义

例句

1.The limiting error in the experiment was found to be within acceptable limits.

实验中的限制误差被发现是在可接受范围内。

2.In statistical analysis, understanding the limiting error is crucial for accurate predictions.

在统计分析中，理解限制误差对于准确预测至关重要。

3.The limiting error can impact the overall performance of the system.

这限制误差可能会影响系统的整体性能。

4.The engineer calculated the limiting error to ensure the precision of the measurements.

工程师计算了限制误差以确保测量的精确性。

5.To improve the reliability of the results, we need to minimize the limiting error.

为了提高结果的可靠性，我们需要最小化限制误差。

作文

In the field of science and engineering, accuracy is paramount. When conducting experiments or making measurements, we often encounter various sources of error that can affect our results. One such concept that is crucial to understanding measurement precision is the limiting error. The term limiting error refers to the maximum possible error in a measurement that can occur under ideal conditions. It provides a boundary within which the true value of a measurement is expected to lie, thus helping scientists and engineers assess the reliability of their data.To illustrate the significance of limiting error, consider a scenario where a researcher is measuring the length of a metal rod using a ruler. If the ruler has a precision of 1 millimeter, the limiting error would be ±0.5 millimeters. This means that the actual length of the rod could be 0.5 millimeters shorter or longer than the measured value. By understanding this limiting error, the researcher can communicate the uncertainty associated with the measurement effectively.Moreover, the concept of limiting error plays a vital role in statistical analysis. In statistics, when calculating the mean of a set of data, the limiting error helps determine the confidence interval. For instance, if a survey is conducted to estimate the average height of a group of individuals, the limiting error will indicate how much the average height could vary from the true average height of the population. This information is crucial for making informed decisions based on the data collected.In engineering applications, limiting error is equally important. Engineers must account for potential errors in their designs to ensure safety and functionality. For example, when designing a bridge, engineers calculate the load-bearing capacity while considering the limiting error associated with material strength measurements. This ensures that the bridge can support the expected loads without failure, even when accounting for uncertainties in the measurements.Furthermore, the limiting error concept extends beyond physical measurements. In computational fields, algorithms and numerical methods also have associated errors. For instance, when performing calculations in computer programming, the limiting error can indicate the maximum deviation that might occur due to rounding errors or approximations. Understanding these errors allows programmers to develop more robust and reliable software.In conclusion, the concept of limiting error is fundamental in various disciplines, including science, engineering, and statistics. It provides a framework for understanding measurement precision and uncertainty, enabling researchers and professionals to make informed decisions based on their data. By recognizing and communicating the limiting error, we can enhance the quality of our work and contribute to advancements in our respective fields. Ultimately, acknowledging the limiting error empowers us to approach problems with a clearer perspective and a greater awareness of the inherent uncertainties in our measurements and calculations.

在科学和工程领域，准确性至关重要。在进行实验或测量时，我们常常会遇到各种可能影响结果的误差源。其中一个对理解测量精度至关重要的概念是极限误差。极限误差这个术语指的是在理想条件下测量中可能发生的最大误差。它提供了一个边界，真实值预计将在此范围内，从而帮助科学家和工程师评估数据的可靠性。为了说明极限误差的重要性，考虑一个研究人员使用尺子测量金属棒长度的场景。如果尺子的精度为1毫米，则极限误差将为±0.5毫米。这意味着金属棒的实际长度可能比测得的值短或长0.5毫米。通过理解这个极限误差，研究人员可以有效地传达与测量相关的不确定性。此外，极限误差的概念在统计分析中也起着至关重要的作用。在统计学中，当计算一组数据的均值时，极限误差有助于确定置信区间。例如，如果进行调查以估计一组个体的平均身高，那么极限误差将指示平均身高可能与真实人口平均身高的偏差。这些信息对于根据收集的数据做出明智的决策至关重要。在工程应用中，极限误差同样重要。工程师必须考虑设计中的潜在误差，以确保安全性和功能性。例如，在设计桥梁时，工程师在计算承载能力时会考虑材料强度测量的极限误差。这确保了桥梁能够支持预期的载荷，而不会因测量的不确定性而失效。此外，极限误差的概念不仅限于物理测量。在计算领域，算法和数值方法也有相关的误差。例如，在计算机编程中进行计算时，极限误差可以指示由于舍入误差或近似导致的最大偏差。理解这些误差使程序员能够开发出更健壮和可靠的软件。总之，极限误差的概念在科学、工程和统计等多个学科中都是基础性的。它提供了理解测量精度和不确定性的框架，使研究人员和专业人士能够根据数据做出明智的决策。通过认识和传达极限误差，我们可以提高工作的质量，并为各自领域的进步做出贡献。最终，承认极限误差使我们能够以更清晰的视角和对测量和计算中固有不确定性的更大意识来解决问题。