absolute value

简明释义

绝对值;

英英释义

例句

1.To find the absolute value of a complex number, you need to calculate the square root of the sum of the squares of its real and imaginary parts.

要找到复数的绝对值，需要计算其实部和虚部平方和的平方根。

2.The absolute value of -5 is 5.

负5的绝对值是5。

3.The formula for the absolute value of a number x can be expressed as |x|.

一个数x的绝对值的公式可以表示为|x|。

4.When calculating the difference between two temperatures, we often use the absolute value to ensure it’s positive.

在计算两个温度之间的差异时，我们通常使用绝对值以确保结果为正。

5.In mathematics, the absolute value of a number represents its distance from zero on the number line.

在数学中，一个数的绝对值表示它在数轴上离零的距离。

作文

The concept of absolute value is fundamental in mathematics, particularly in the study of numbers and their properties. The absolute value of a number is defined as its distance from zero on the number line, regardless of direction. This means that both positive and negative numbers have the same absolute value. For example, the absolute value of -5 is 5, and the absolute value of 5 is also 5. This property makes absolute value a useful tool in various mathematical applications, including algebra, calculus, and even in real-world scenarios.Understanding absolute value is crucial for solving equations and inequalities. When we encounter an equation like |x| = 3, we need to recognize that this means x can be either 3 or -3. This duality is essential for finding all possible solutions to the equation. Similarly, when dealing with inequalities, such as |x| < 4, we understand that x must lie between -4 and 4. Thus, mastering the concept of absolute value allows us to approach problems with greater confidence and accuracy.Moreover, absolute value finds applications beyond pure mathematics. In fields such as physics and engineering, it helps in measuring quantities that cannot be negative, such as distance, speed, and force. For instance, if a car travels 60 kilometers east and then 60 kilometers west, the total displacement is zero, but the total distance traveled is 120 kilometers. Here, the absolute value plays a role in determining the actual distance covered, which is always a non-negative quantity.In computer science, the concept of absolute value is frequently used in algorithms and programming. When developing software that involves numerical computations, programmers often need to ensure that certain values remain non-negative. By using the absolute value function, they can easily convert any negative input into a positive one, thus preventing errors in calculations or data processing.Furthermore, the absolute value is significant in statistics, particularly in the calculation of deviations and errors. When analyzing data, researchers often look at the deviation of individual data points from the mean. Using absolute value allows them to quantify these deviations without regard to whether they are above or below the mean, providing a clearer picture of variability within the data set.In conclusion, the concept of absolute value is not only a key mathematical principle but also a versatile tool applied across various disciplines. Its ability to simplify complex problems and provide clarity in measurement makes it invaluable in both academic and practical contexts. By understanding and applying the concept of absolute value, we enhance our problem-solving skills and deepen our comprehension of the world around us. Whether in mathematics, science, or everyday life, the absolute value remains a powerful concept that underscores the importance of distance and magnitude in our analyses and decisions.

绝对值的概念在数学中是基础性的，特别是在数字及其属性的研究中。一个数字的绝对值被定义为它在数轴上距离零的距离，无论方向如何。这意味着正数和负数有相同的绝对值。例如，-5的绝对值是5，而5的绝对值也是5。这一特性使得绝对值成为各种数学应用中的有用工具，包括代数、微积分，甚至在现实场景中。理解绝对值对于解决方程和不等式至关重要。当我们遇到一个方程如|x| = 3时，我们需要认识到这意味着x可以是3或-3。这种二元性对于找到方程的所有可能解是必不可少的。同样，在处理不等式时，例如|x| < 4，我们理解x必须位于-4和4之间。因此，掌握绝对值的概念使我们能够更自信、更准确地处理问题。此外，绝对值在纯数学之外的应用也很广泛。在物理学和工程学等领域，它帮助测量不能为负的量，如距离、速度和力。例如，如果一辆车向东行驶60公里，然后向西行驶60公里，总位移为零，但总行驶距离为120公里。在这里，绝对值在确定实际行驶距离时起着作用，这始终是一个非负量。在计算机科学中，绝对值的概念经常用于算法和编程。在开发涉及数值计算的软件时，程序员通常需要确保某些值保持非负。通过使用绝对值函数，他们可以轻松地将任何负输入转换为正数，从而防止计算或数据处理中的错误。此外，绝对值在统计学中也很重要，特别是在偏差和误差的计算中。当分析数据时，研究人员通常会查看单个数据点与均值的偏差。使用绝对值可以让他们量化这些偏差，而不考虑它们是高于还是低于均值，从而提供更清晰的数据集变异性图景。总之，绝对值的概念不仅是一个关键的数学原理，也是一个在各个学科中应用广泛的多功能工具。它简化复杂问题和在测量中提供清晰度的能力使其在学术和实践背景中都具有不可或缺的价值。通过理解和应用绝对值的概念，我们增强了问题解决能力，加深了对周围世界的理解。无论是在数学、科学还是日常生活中，绝对值仍然是一个强大的概念，强调了我们分析和决策中距离和大小的重要性。