What are the basic concepts of pure cyclic decimal and mixed cyclic decimal?

1, and the cyclic decimal starting from the first decimal part is called pure cyclic decimal. Pure circulating decimal is a decimal that circulates from decimal, such as 0.33333333 ... (1/3), 0.1428 571428 571... (1/7) and so on. As the name implies, pure cyclic decimal is a cyclic decimal based on pure decimal.

2. The cycle segment does not start from the first digit of the decimal part, which is called mixed cycle decimal. For example: 1.333, 13, etc. We can observe that 1.23333 has more than 3 cyclic nodes.

Extended data

1, the number of decimal places is limited, which is called finite decimal; The number of digits in the decimal part is infinite decimal, which is called infinite decimal. Cyclic decimal is infinite decimal.

2. The decimal part of the cyclic decimal, that is, the number that appears repeatedly in turn, is called the cyclic segment of this cyclic decimal. For example, the period part of 5.33 is 3. 7. The cycle segment of14545 is 45.

3. If the cycle segment starts from the first digit of the decimal part, it is called a pure cycle decimal; The cycle segment does not start from the first digit of the decimal part, which is called mixed cycle decimal.

4. Simple notation of circulating decimals: omit the ""sign behind it and add a few points in the first circulating segment. Such as: 5.33=5.3, which is read as a cycle of 5.3 and 3; 7. 14545=7. 145, pronounced as 7. 145 and 4.5 cycles. If there are three or more periods, put numbers at the beginning and end points. Such as 7.123123 = 7.123.

Baidu Encyclopedia-Pure Cyclic Decimal

Baidu Encyclopedia-Mixed Cycle Decimal