repeating decimal fraction

简明释义

循环小数

英英释义

例句

1.When dividing 1 by 3, the result is a repeating decimal fraction 循环小数 of 0.333...

当将1除以3时，结果是一个循环小数0.333...

2.The decimal 0.666... is an example of a repeating decimal fraction 循环小数 that equals 2/3.

小数0.666...是一个循环小数的例子，它等于2/3。

3.To simplify calculations, you should know how to handle repeating decimal fractions 循环小数 effectively.

为了简化计算，你应该知道如何有效处理循环小数。

4.Some students find it challenging to convert a repeating decimal fraction 循环小数 into a fraction form.

一些学生发现将循环小数转换为分数形式很有挑战性。

5.In mathematics, a repeating decimal fraction 循环小数 can be represented with a bar over the repeating part.

在数学中，循环小数可以用重复部分上方的横线表示。

作文

Understanding the concept of a repeating decimal fraction is essential for anyone studying mathematics or dealing with numerical calculations. A repeating decimal fraction is a type of decimal that continues infinitely with a repeating pattern of digits. For example, the fraction 1/3 equals 0.333..., where the digit '3' repeats indefinitely. This can be expressed as a repeating decimal fraction because it does not terminate but rather continues on forever in the same sequence. To grasp the significance of repeating decimal fractions, we must first understand how they are formed. When a fraction is divided, the result can either be a terminating decimal or a repeating decimal. Terminating decimals have a finite number of digits after the decimal point, such as 0.25 or 0.5. In contrast, repeating decimal fractions arise when the division of two integers results in a remainder that leads to the same quotient being calculated repeatedly.For instance, consider the fraction 2/11. When you divide 2 by 11, you get 0.181818..., where '18' is the repeating part. This means that the repeating decimal fraction can be written as 0.1̅8̅, indicating that '18' repeats endlessly. Understanding this allows us to convert fractions into their decimal forms and vice versa, which is a crucial skill in mathematics.Moreover, repeating decimal fractions can also be represented algebraically. If we let x equal a repeating decimal fraction like 0.666..., we can set up an equation to find its fractional equivalent. By multiplying both sides of the equation by 10, we get 10x = 6.666..., and then subtracting the original x from this equation gives us 9x = 6. This simplifies to x = 6/9, which can be reduced to 2/3. Thus, we see that the repeating decimal fraction 0.666... is equal to the fraction 2/3. The understanding of repeating decimal fractions is not just limited to theoretical mathematics; it has practical applications as well. In real-world scenarios, many measurements and calculations involve repeating decimals. For example, in finance, interest rates may sometimes be expressed as repeating decimal fractions. Recognizing these can help individuals make informed decisions about loans and investments.In conclusion, the concept of repeating decimal fractions is a fascinating aspect of mathematics that bridges the gap between fractions and decimals. It provides a deeper insight into how numbers behave when divided and helps us to understand the infinite nature of some decimal representations. Whether in academic studies or everyday life, being able to identify and work with repeating decimal fractions is a valuable skill that enhances numerical literacy and problem-solving abilities. Therefore, embracing this concept can empower individuals in various fields, making them more adept at handling mathematical challenges.

理解循环小数分数的概念对任何学习数学或进行数字计算的人来说都是至关重要的。循环小数分数是一种小数，它以重复的数字模式无限延续。例如，分数1/3等于0.333...，其中数字'3'无限重复。这可以表示为循环小数分数，因为它不会终止，而是永远以相同的序列继续下去。要掌握循环小数分数的重要性，我们必须首先了解它们是如何形成的。当一个分数被除时，结果可以是终止小数或循环小数。终止小数在小数点后有有限数量的数字，例如0.25或0.5。相反，循环小数分数出现于两个整数的除法结果导致余数，使得相同的商被重复计算。例如，考虑分数2/11。当你将2除以11时，你得到0.181818...，其中'18'是重复部分。这意味着循环小数分数可以写成0.1̅8̅，表示'18'无休止地重复。理解这一点使我们能够将分数转换为其小数形式，反之亦然，这在数学中是一项关键技能。此外，循环小数分数也可以用代数表示。如果我们让x等于一个循环小数分数，比如0.666...，我们可以建立一个方程来找出它的分数等价物。通过将方程两边都乘以10，我们得到10x = 6.666...，然后从这个方程中减去原来的x，得到9x = 6。这简化为x = 6/9，可以约简为2/3。因此，我们看到循环小数分数0.666...等于分数2/3。对循环小数分数的理解不仅限于理论数学；它也有实际应用。在现实世界的场景中，许多测量和计算涉及循环小数。例如，在金融领域，利率有时会表示为循环小数分数。认识到这些可以帮助个人在贷款和投资方面做出明智的决定。总之，循环小数分数的概念是数学中一个迷人的方面，它弥合了分数和小数之间的差距。它提供了更深入的见解，了解数字在除法时的行为，并帮助我们理解某些小数表示的无限性质。无论是在学术研究还是日常生活中，能够识别和处理循环小数分数是一项有价值的技能，可以增强数字素养和解决问题的能力。因此，接受这一概念可以使个人在各个领域更具能力，使他们更善于应对数学挑战。