rational number

简明释义

有理数

英英释义

例句

1.In mathematics, rational numbers include integers, fractions, and terminating decimals.

在数学中，有理数包括整数、分数和有限小数。

2.When dividing a pizza into equal slices, each slice represents a rational number of the whole.

当把比萨饼切成相等的片时，每一片代表整个比萨饼的一个有理数。

3.A rational number is any number that can be expressed as a fraction, such as 1/2 or 3/4.

一个有理数是可以表示为分数的任何数字，例如1/2或3/4。

4.The decimal 0.75 is a rational number because it can be written as 3/4.

小数0.75是一个有理数，因为它可以写成3/4。

5.To solve this equation, you need to find a rational number that satisfies it.

要解决这个方程，你需要找到一个满足它的有理数。

作文

In the realm of mathematics, numbers are categorized into various types, each serving a unique purpose. One fundamental category is that of the rational number, which plays a crucial role in our understanding of numerical systems. A rational number is defined as any number that can be expressed as the quotient or fraction of two integers, where the numerator is an integer and the denominator is a non-zero integer. This means that every rational number can be written in the form a/b, where 'a' and 'b' are integers and b ≠ 0.Understanding rational numbers is essential for many areas of mathematics. For instance, when performing basic arithmetic operations such as addition, subtraction, multiplication, and division, rational numbers provide a foundation for more complex calculations. They allow us to solve equations and understand relationships between quantities. Additionally, rational numbers can be represented on a number line, making it easier to visualize their placement relative to other numbers, including integers and irrational numbers.One interesting aspect of rational numbers is their density on the number line. Between any two rational numbers, there exists another rational number. This property demonstrates that rational numbers are abundant and can be found almost anywhere within the continuum of real numbers. For example, between the rational numbers 1/2 and 1/3, we can find 5/12, which is also a rational number. This characteristic highlights the infinite nature of rational numbers despite being countable.Moreover, rational numbers can also be expressed in decimal form. Some rational numbers have terminating decimals, such as 0.75, while others have repeating decimals, like 1/3, which is represented as 0.333... This distinction is important because it shows how rational numbers can be interpreted in different ways, depending on the context in which they are used.In practical applications, rational numbers are prevalent in various fields, including science, engineering, finance, and everyday life. For instance, when calculating interest rates or determining proportions in recipes, rational numbers come into play frequently. Their ability to represent precise values makes them invaluable in both theoretical and applied mathematics.Despite their significance, it is essential to recognize that rational numbers are only one part of the broader number system. They coexist with irrational numbers, which cannot be expressed as fractions of integers, such as the square root of 2 or pi. The interplay between rational numbers and irrational numbers enriches our understanding of mathematics and its applications.In conclusion, rational numbers are a foundational element of mathematics, offering a framework for understanding numerical relationships and performing calculations. Their properties, such as density and the ability to be expressed in various forms, make them essential in both theoretical and practical contexts. As we continue to explore the world of numbers, appreciating the role of rational numbers will enhance our mathematical literacy and problem-solving skills.

在数学领域，数字被分为各种类型，每种类型都有其独特的用途。一个基本的类别是有理数，它在我们理解数字系统中起着至关重要的作用。有理数的定义是可以表示为两个整数的商或分数的任何数字，其中分子是整数，分母是非零整数。这意味着每个有理数都可以写成a/b的形式，其中'a'和'b'是整数，并且b ≠ 0。理解有理数对于许多数学领域至关重要。例如，在进行基本算术运算如加法、减法、乘法和除法时，有理数为更复杂的计算提供了基础。它们使我们能够解决方程并理解数量之间的关系。此外，有理数可以在数轴上表示，使我们更容易可视化它们相对于其他数字（包括整数和无理数）的放置。有理数的一个有趣方面是它们在数轴上的密度。在任何两个有理数之间，都存在另一个有理数。这一特性表明有理数是丰富的，并且几乎可以在实数的连续体中找到。例如，在有理数1/2和1/3之间，我们可以找到5/12，这也是一个有理数。这一特征突显了有理数的无限性，尽管它们是可数的。此外，有理数也可以用小数形式表示。一些有理数具有终止小数，比如0.75，而其他一些则具有重复小数，如1/3，其表示为0.333...。这种区别很重要，因为它展示了有理数可以以不同的方式进行解释，具体取决于使用的上下文。在实际应用中，有理数在科学、工程、金融和日常生活等各个领域中普遍存在。例如，在计算利率或确定食谱中的比例时，有理数经常发挥作用。它们能够代表精确值，使其在理论和应用数学中都不可或缺。尽管有理数具有重要意义，但必须认识到它们只是更广泛数字系统的一部分。它们与无法表示为整数分数的无理数共存，例如平方根2或π。有理数与无理数之间的相互作用丰富了我们对数学及其应用的理解。总之，有理数是数学的基础元素，为理解数字关系和进行计算提供了框架。它们的性质，如密度和以各种形式表达的能力，使它们在理论和实践中都至关重要。随着我们继续探索数字的世界，欣赏有理数的作用将增强我们的数学素养和解决问题的能力。