What is a cyclic decimal?

The decimal part of a number is an infinite decimal that one or several numbers repeat in turn from a certain bit, which is called a cyclic decimal. Among them, the numbers that appear repeatedly in turn are called cyclic knots.

Cyclic decimals have cyclic nodes (cyclic points), which can be turned into fractions.

If two integers are divided, if the integer quotient cannot be obtained, there will be two situations: one is to get a finite decimal; The other is to get infinite decimals.

The abbreviation of cyclic decimal is to omit all the digits after the first cyclic segment, and add a dot above the first two digits and the last two digits of the first cyclic segment.

Extended data

First of all, the rule of dividing the decimal part of the circulating decimal into several parts

1, fractional component number of pure cyclic decimal: the numerator is the number composed of the number of a cyclic segment, all digits of the denominator are 9, and the number of 9 is the same as the number of cyclic segments, and it can be reduced again at last.

2. Number of decimal parts in mixed cycle: the numerator is the difference between the number of decimal parts before the second cycle and the number of acyclic parts. The first few digits of the denominator are 9, the number of 9 is the same as that of the cyclic segment, and the last few digits are 0, and the number of 0 is the same as that of the acyclic part.

Second, the judgment method of decimal conversion into cyclic decimal:

1, the simplest fraction, if the denominator contains both prime factors 2 and 5 and prime factors other than prime factors 2 and 5, then this fraction must be a mixed cyclic decimal.

2, the simplest fraction, if the denominator only contains prime factors other than 2 and 5, then this fractional decimal must be a pure cyclic decimal.

Baidu Encyclopedia-Cyclic Decimal