relative error

简明释义

相对误差

英英释义

例句

1.A low relative error 相对误差 indicates high precision in measurements.

低相对误差 相对误差表明测量的高精度。

2.In scientific experiments, it is crucial to minimize the relative error 相对误差 to ensure accurate results.

在科学实验中，减少相对误差 相对误差至关重要，以确保结果的准确性。

3.When calculating the relative error 相对误差, it is important to compare the error to the true value.

在计算相对误差 相对误差时，重要的是将误差与真实值进行比较。

4.The measurement of the length of the table had a relative error 相对误差 of 2%, which is acceptable for our purposes.

桌子的长度测量有一个相对误差 相对误差为2%，这对于我们的目的来说是可以接受的。

5.The relative error 相对误差 in the density measurement was found to be 1.5%.

密度测量中的相对误差 相对误差被发现为1.5%。

作文

In the field of science and engineering, precision is crucial. One important concept that helps us quantify the accuracy of our measurements is known as relative error. The term relative error refers to the difference between a measured value and a true or accepted value, expressed as a fraction of the true value. This metric is essential because it provides context to the error by relating it to the size of the measurement itself. For instance, if we measure the length of an object to be 10 cm, but the actual length is 9.5 cm, the absolute error is 0.5 cm. However, the relative error would be calculated as the absolute error divided by the true value, which in this case would be 0.5 cm / 9.5 cm, resulting in approximately 0.0526 or 5.26%. This means that the error is about 5.26% of the true value, giving us a clearer picture of how significant the error is in relation to the measurement.Understanding relative error is particularly important in fields such as physics and engineering, where small inaccuracies can lead to significant consequences. For example, in engineering design, if the dimensions of a component are slightly off, it could lead to failure in a machine or structure. By calculating the relative error, engineers can assess whether their measurements are within acceptable limits and make necessary adjustments.Moreover, relative error is not only relevant in experimental sciences but also in various applications like finance, economics, and statistics. In these fields, analysts often deal with large datasets and need to ensure that their calculations and forecasts are accurate. A small relative error in financial predictions can translate into substantial monetary losses or gains, making it imperative for analysts to minimize errors.It is also worth noting that relative error can be influenced by several factors including the precision of measuring instruments, the methodology used during data collection, and even human error. For instance, a digital scale may have a specific tolerance level, which can affect the relative error of weight measurements. Understanding the sources of error can help researchers and professionals improve their techniques and reduce the relative error in their work.In conclusion, the concept of relative error is fundamental to evaluating the accuracy of measurements across various disciplines. It allows scientists, engineers, and analysts to communicate the significance of their findings and the reliability of their data. By keeping relative error in mind, professionals can strive for greater precision and ultimately achieve better outcomes in their respective fields. As we continue to advance in technology and methodology, understanding and minimizing relative error will remain a key component of scientific inquiry and practical application. Thus, mastering the concept of relative error is essential for anyone involved in quantitative analysis, ensuring that we can trust our measurements and the conclusions drawn from them.

在科学和工程领域，精确性至关重要。一个帮助我们量化测量准确性的重要概念被称为相对误差。术语相对误差指的是测量值与真实或接受值之间的差异，以真实值的分数形式表示。这个指标是必不可少的，因为它通过将误差与测量本身的大小联系起来，为误差提供了背景。例如，如果我们测量一个物体的长度为10厘米，但实际长度为9.5厘米，那么绝对误差为0.5厘米。然而，相对误差将被计算为绝对误差除以真实值，在这种情况下为0.5厘米/9.5厘米，结果约为0.0526或5.26%。这意味着误差约为真实值的5.26%，使我们更清楚地了解误差在测量中所占的重要性。理解相对误差在物理学和工程等领域尤为重要，因为小的不准确性可能导致重大后果。例如，在工程设计中，如果组件的尺寸稍有偏差，可能导致机器或结构的故障。通过计算相对误差，工程师可以评估他们的测量是否在可接受的范围内，并进行必要的调整。此外，相对误差不仅在实验科学中相关，在金融、经济和统计等各个应用中也同样重要。在这些领域，分析师通常处理大量数据集，需要确保他们的计算和预测是准确的。金融预测中的小相对误差可能会转化为巨大的货币损失或收益，因此分析师必须尽量减少错误。还值得注意的是，相对误差可能受到多种因素的影响，包括测量仪器的精度、数据收集过程中使用的方法，甚至是人为错误。例如，数字秤可能具有特定的公差水平，这可能影响重量测量的相对误差。了解误差来源可以帮助研究人员和专业人士改善他们的技术并减少工作中的相对误差。总之，相对误差的概念对于评估各个学科中测量的准确性是基础。它使科学家、工程师和分析师能够传达他们发现的意义及其数据的可靠性。通过牢记相对误差，专业人士可以努力追求更高的精确度，最终在各自的领域取得更好的成果。随着我们在技术和方法上的不断进步，理解和最小化相对误差将始终是科学探究和实际应用的关键组成部分。因此，掌握相对误差的概念对于任何参与定量分析的人来说都是必不可少的，确保我们可以信任我们的测量及其得出的结论。