This is because the definition of circular decimal is a decimal, and a number repeats somewhere after the decimal point. This number can be one, two, three or even more digits, but it always appears repeatedly and endlessly.

For example, 1/3 is a cyclic decimal, which is equal to 0.333 ... (a cycle of 3). Every digit after the decimal point is 3, and this number will repeat indefinitely and will never end. Similarly, 1/7 is also a cyclic decimal, which is equal to 0.1428 57142857 ... (the cycle of142857), and every digit after the decimal point is a constant repetition of these six numbers.

Because the cyclic decimal repeats a number all the time, there is no last decimal place, that is to say, its decimal part is infinite. Therefore, all recurring decimals are infinite decimals.

Note that not all infinite decimals are cyclic decimals. For example, π (pi) is an infinite acyclic decimal, and new numbers keep appearing in its decimal part, with no obvious regularity and repetition pattern. However, there is no doubt that all recurring decimals are infinite decimals.

The importance of learning mathematics;

1. Mathematics is a basic subject and the cornerstone of natural science, social science, engineering technology and other fields. Mathematical methods are widely used in scientific research, engineering design and economic analysis. By studying mathematics, we can cultivate logical thinking ability, abstract thinking ability, reasoning ability and problem-solving ability, which are very important for work and study in various fields.

2. Mathematics is also widely used in daily life. Mathematics is everywhere, from discount calculation when shopping, to the best route selection when planning a trip, to the risk assessment of investment and financial management. Mastering mathematics knowledge can help us better understand and solve problems in life.

3. Mathematics learning can also cultivate people's morality and quality. Through mathematics training, we can cultivate rigorous, meticulous, patient and tenacious qualities, which are very important for personal growth and development.

4. Mathematics is also a subject with aesthetic value. The beauty of symmetry, simplicity and harmony in mathematics makes people feel the charm of mathematics. By studying mathematics, we can cultivate aesthetic ability and creativity, which is also an important value of mathematics learning.