What is a cyclic decimal and what is a cyclic decimal What is a cyclic decimal

The decimal part of a number starts from a certain digit, and the infinite decimal number of one or several numbers repeating in turn is called a cyclic decimal. Loop decimal will have loop knots (loop points). When two integers are divided, if the integer quotient is not obtained, there are two cases:

one, to get a finite decimal; The other, get an infinite decimal. The decimal infinite decimal of the previous one or a section of numbers is called a cyclic decimal number, such as a mixed cyclic decimal place), a cyclic decimal), a cyclic decimal), etc., in which the number that recurs in turn is called a cyclic section. The abbreviation for cyclic decimal is to omit all the numbers after the first cyclic stanza and add a small dot above the first and last two digits of the first cyclic stanza.

1] For example, the abbreviation is OR (pronounced as "2.96, 6 cycles") abbreviated as OR (it is pronounced as "35.23, 23 cycles") abbreviated as OR (it is pronounced "36.568, 5-8 cycles") Cyclic decimals can be converted into fractions using the method of summation formula for proportional sequences (link: Proportional sequences), so cyclic decimals are rational numbers.

You can convert fractions to fractions.

What is a cyclic decimal?

Let's talk about how to convert cyclic decimals into fractions.

Infinite cyclic decimal numbers are divided into 2 categories, one is pure cyclic decimals;

The other type is mixed loop decimals.

Infinite looping decimals can be converted into fractions.

1. Pure cyclic decimals are converted into fractionsWhat is a pure cyclic decimal?

The decimal that starts the cycle from the first decimal place after the decimal point is called a pure cyclic decimal number.

2. Convert mixed circulation decimal into fractionsA decimal that does not start a loop with the first decimal place after the decimal point is called a mixed circular decimal number.

Summary

Generally, the infinite loop decimal conversion into fractions can be converted by the above methods, summarize its rules, and the next time you can directly convert, which is very convenient.

Of course, the loop section can be 3 digits, 4 digits, 5 digits, according to the above method, you can apply the formula to convert.

If you think it's useful, take the formula.

1. The decimal part of a number is called a circular decimal from a certain auspicious god, and the infinite decimal number that repeats one or several numbers in turn is called a circular decimal. Cyclic decimals have loop knots (loop points) and can be converted into fractions.

2. 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, get an infinite decimal.

3. The decimal infinite good rush decimal number of the previous one or a section of numbers begins to repeat in turn after a certain digit after the decimal point, which is called a cyclic decimal, such as a mixed cyclic decimal), a cyclic decimal), a cyclic decimal), etc., in which the number that recurs in turn is called a cyclic section.

What is a cyclic decimal1.When a decimal part of a number starts from a certain position, an infinitesimal attack block number in which one or several numbers repeat in turn is called a cyclic decimal number. Zen guess that circular decimal numbers have circular parts (dots) that can be converted into fractions.

2.Put two integers. If you can't get the integer quotient, there are two situations: one is to get a finite decimal; Another way is to get an infinitesimal decimal.

3.The decimal point of the previous digit or a segment of numbers is repeated sequentially after the decimal point, and the position after the decimal point is repeated, which is called a cyclic decimal, such as mixed cyclic decimal system), cyclic decimal), cyclic decimal), etc., where the number that repeats sequentially is called a cyclic decimal.