circulating decimal

简明释义

循环小数

英英释义

例句

1.When converting fractions to decimals, it's important to recognize if the result is a circulating decimal.

在将分数转换为小数时，识别结果是否为循环小数是很重要的。

2.The fraction 1/3 can be expressed as a circulating decimal, which is 0.333..., where the 3 repeats indefinitely.

分数1/3可以表示为一个循环小数，即0.333...，其中3无限重复。

3.The circulating decimal 0.666... is equal to the fraction 2/3.

循环小数0.666...等于分数2/3。

4.In mathematics, a circulating decimal can be represented using a bar notation over the repeating digits.

在数学中，循环小数可以用重复数字上方的横线表示。

5.Understanding circulating decimals helps students grasp the concept of infinite series.

理解循环小数有助于学生掌握无限级数的概念。

作文

Understanding the concept of a circulating decimal is essential in the field of mathematics, particularly in number theory. A circulating decimal refers to a decimal fraction that eventually repeats a sequence of digits indefinitely. For instance, the decimal representation of one-third, which is 0.333..., is an example of a circulating decimal. In this case, the digit '3' continues infinitely, indicating that it is a repeating decimal. The significance of circulating decimals extends beyond mere numerical representation; they play a crucial role in various mathematical operations and concepts. When performing arithmetic operations such as addition, subtraction, multiplication, or division with circulating decimals, one must be cautious about how to handle the repeating parts. This can often lead to confusion among students who are new to the concept. To illustrate further, consider the example of 0.666..., which can also be expressed as 2/3. The circulating decimal here is '6', which repeats indefinitely. Understanding that this decimal represents a rational number is vital. Rational numbers can be expressed as fractions, and recognizing circulating decimals as such helps in simplifying complex calculations. Moreover, circulating decimals can be converted into fractions, which is a useful skill in mathematics. For example, if we take the circulating decimal 0.142857..., we can identify that it corresponds to the fraction 1/7. This conversion process involves setting the decimal equal to a variable, multiplying by a power of ten to shift the decimal point, and then solving for the variable. This method not only reinforces understanding but also enhances problem-solving skills. In real-world applications, circulating decimals can be found in various scenarios, such as financial calculations, measurements, and data analysis. For instance, when dealing with interest rates, one might encounter circulating decimals while calculating compound interest. Being able to accurately interpret these decimals is essential for making sound financial decisions. Furthermore, the study of circulating decimals introduces learners to the broader topic of irrational numbers and their differences from rational numbers. While circulating decimals can be expressed as fractions, irrational numbers cannot be represented in such a way. This distinction is fundamental in understanding the number system as a whole. In conclusion, mastering the concept of circulating decimals is more than just memorizing definitions; it involves developing a deeper understanding of how these decimals function within the realm of mathematics. Whether it’s through practical applications or theoretical exploration, the knowledge of circulating decimals equips students with valuable skills that will aid them in their academic and professional journeys. By recognizing the importance of circulating decimals, we can appreciate the elegance and complexity of numbers in our everyday lives.

理解循环小数的概念在数学领域，尤其是数论中是至关重要的。循环小数指的是一个十进制分数，它最终会无限重复一组数字。例如，三分之一的十进制表示是0.333...，这是一个循环小数的例子。在这种情况下，数字'3'不断延续，表明它是一个重复的小数。循环小数的意义不仅仅在于数字的表示；它们在各种数学运算和概念中发挥着关键作用。当进行加法、减法、乘法或除法等算术运算时，处理循环小数的重复部分时必须小心。这常常会导致对这个概念不熟悉的学生感到困惑。进一步说明，考虑0.666...的例子，它也可以表示为2/3。这里的循环小数是'6'，它无限重复。理解这个小数代表一个有理数是至关重要的。有理数可以表示为分数，认识到循环小数是这样的有助于简化复杂的计算。此外，循环小数可以转换为分数，这在数学中是一项有用的技能。例如，如果我们取循环小数0.142857...，我们可以识别出它对应于分数1/7。这个转换过程涉及将小数设置为一个变量，乘以10的幂以移动小数点，然后求解该变量。这个方法不仅增强了理解，还提高了问题解决能力。在现实应用中，循环小数可以在各种场景中找到，例如财务计算、测量和数据分析。例如，在处理利率时，计算复利时可能会遇到循环小数。准确解释这些小数对于做出明智的财务决策至关重要。此外，研究循环小数还引导学习者了解有理数和无理数之间的更广泛主题。虽然循环小数可以表示为分数，但无理数无法以这种方式表示。这一区别对于理解整个数字系统是基础的。总之，掌握循环小数的概念不仅仅是记住定义；它涉及深入理解这些小数在数学领域中的运作方式。无论是通过实际应用还是理论探索，了解循环小数使学生具备了在学术和职业旅程中有价值的技能。通过认识到循环小数的重要性，我们可以欣赏到数字在日常生活中的优雅与复杂性。