relative error

简明释义

相对误差

英英释义

例句

1.To improve accuracy, engineers aim to reduce the relative error in their measurements to less than 0.5%.

为了提高准确性，工程师们力求将测量中的相对误差降低到0.5%以下。

2.When calculating the speed of the vehicle, we found a relative error of 1.5% due to rounding.

在计算车辆速度时，由于四舍五入，我们发现了1.5%的相对误差。

3.In scientific experiments, it is crucial to minimize the relative error to ensure accurate results.

在科学实验中，减少相对误差至关重要，以确保结果的准确性。

4.The measurement of the length of the table showed a relative error of 2%, indicating that the actual length was slightly different from the measured value.

桌子的长度测量显示出一个相对误差为2%，这表明实际长度与测量值略有不同。

5.The relative error in the temperature readings can affect the overall conclusions of the study.

温度读数中的相对误差会影响研究的整体结论。

作文

In the field of science and engineering, accuracy is paramount. When we make measurements, it is essential to understand how precise those measurements are. One way to quantify the accuracy of a measurement is through the concept of relative error. The term relative error refers to the difference between the measured value and the true value, expressed as a fraction of the true value. This concept is crucial because it allows us to assess the significance of the error in relation to the size of the measurement itself.For instance, consider an experiment where we measure the length of a table to be 100 cm, but the actual length is 102 cm. The absolute error in this case is 2 cm. However, to understand how significant this error is, we can calculate the relative error. The relative error is calculated by taking the absolute error and dividing it by the true value. In our example, the relative error would be 2 cm divided by 102 cm, which gives approximately 0.0196 or 1.96%. This means that the error is about 1.96% of the true length of the table, providing a clearer picture of the measurement's accuracy.The importance of relative error becomes even more apparent when we compare measurements of different magnitudes. For instance, if we measure the height of a building as 50 meters with a possible error of 1 meter, the relative error would be 1/50 = 0.02 or 2%. On the other hand, if we measure the height of a small object, say a pencil, to be 20 cm with the same possible error of 1 cm, the relative error would be 1/20 = 0.05 or 5%. This comparison shows that while the absolute error is the same (1 unit), the relative error is significantly larger for the smaller measurement, highlighting the importance of considering the scale of the measurement when evaluating accuracy.In many scientific experiments, the relative error helps researchers determine whether their results are reliable. A small relative error indicates that the measurement is close to the true value, while a large relative error suggests that the measurement may not be trustworthy. Therefore, researchers often aim to minimize relative error in their experiments to ensure that their findings are valid and can be replicated.Moreover, the concept of relative error extends beyond just physical measurements. It is also applicable in fields such as finance, where analysts may look at the relative error of predicted financial outcomes versus actual results. Understanding relative error in these contexts can provide insights into the reliability of forecasts and models.In conclusion, the concept of relative error is fundamental in evaluating the accuracy of measurements across various fields. By understanding how relative error is calculated and its significance, we can better interpret data and make informed decisions based on our findings. Whether in scientific research, engineering, or finance, recognizing the implications of relative error enables us to strive for precision and reliability in our work. Thus, mastering the understanding of relative error is essential for anyone engaged in quantitative analysis and measurement.

在科学和工程领域，准确性至关重要。当我们进行测量时，了解这些测量的精确程度是非常必要的。量化测量准确性的一种方法是通过相对误差的概念。术语相对误差指的是测量值与真实值之间的差异，以真实值的分数形式表示。这个概念至关重要，因为它使我们能够评估误差相对于测量本身大小的重要性。例如，考虑一个实验，我们测量一张桌子的长度为100厘米，但实际长度为102厘米。在这种情况下，绝对误差为2厘米。然而，为了了解这个误差的重要性，我们可以计算相对误差。相对误差是通过将绝对误差除以真实值来计算的。在我们的例子中，相对误差将是2厘米除以102厘米，大约等于0.0196或1.96%。这意味着误差约占桌子真实长度的1.96%，提供了测量准确性的更清晰的图景。当我们比较不同数量级的测量时，相对误差的重要性变得更加明显。例如，如果我们测量一栋建筑的高度为50米，可能的误差为1米，则相对误差将是1/50 = 0.02或2%。另一方面，如果我们测量一个小物体，比如一支铅笔，高度为20厘米，可能的误差为1厘米，则相对误差将是1/20 = 0.05或5%。这个比较表明，尽管绝对误差是相同的（1个单位），但对于较小的测量，相对误差显著更大，突显了在评估准确性时考虑测量规模的重要性。在许多科学实验中，相对误差帮助研究人员确定他们的结果是否可靠。小的相对误差表明测量接近真实值，而大的相对误差则表明测量可能不可信。因此，研究人员通常力求在实验中最小化相对误差，以确保他们的发现有效且可重复。此外，相对误差的概念不仅适用于物理测量。在金融等领域，分析师也可能会查看预测财务结果与实际结果的相对误差。在这些背景下理解相对误差可以提供对预测和模型可靠性的洞察。总之，相对误差的概念在各个领域评估测量准确性方面是基础性的。通过理解相对误差的计算方式及其重要性，我们可以更好地解释数据并基于我们的发现做出明智的决策。无论是在科学研究、工程还是金融领域，认识到相对误差的影响使我们能够在工作中追求精确性和可靠性。因此，掌握对相对误差的理解对于任何从事定量分析和测量的人来说都是至关重要的。