Cyclic decimal refers to an infinite decimal in which the decimal part of a number starts from a certain bit and one or several numbers appear repeatedly in turn. 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. Decimal Infinite Decimal, in which the previous digit or a segment of digits repeats from a certain digit after the decimal point, is called cyclic decimal.
For example, 2. 1666...* (mixed cyclic decimal), 35.232323 ... (cyclic decimal), 20.333333 ... (cyclic decimal), etc. , in which the numbers that appear repeatedly in turn are called cyclic segments. 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.
The mixed cyclic decimal is rewritten as a component number, and the numerator is a number composed of the acyclic part and the number connected with the first cyclic node, minus the difference of the number composed of the acyclic part; The first few digits of the denominator are 9 and the last few digits are 0. The number of 9 is the same as the number of cyclic parts, and the number of 0 is the same as the number of acyclic parts.
The benefits of learning mathematics:
1. Mathematics can cultivate people's integrity and honesty. Mathematics pays the most attention to convincing people by reasoning, and only believes in the results of logical reasoning.
Mathematics can cultivate people's tenacity and courage. Paulia, a great math educator, thinks that difficulties and problems belong to the same concept. If there is no difficulty, there will be no problem.
3. Mathematics can cultivate people's overall consciousness. To solve mathematical problems, we must comprehensively consider the problems from the known to the conclusion and grasp the interrelationships of all aspects. Mathematics teaching can cultivate students to consider problems comprehensively from the overall situation.
Mathematics can cultivate people's good character. The better a person's math study, the more flexible his thinking. In this case, his enthusiasm and enthusiasm are very high, and he is good at expressing his ideas and methods, so that his communication skills will be tempered and his self-confidence will be gradually enhanced.