Infinitely circulating decimal refers to the situation that one or more numbers appear repeatedly in the decimal part. This cycle can be a single number cycle or a group of number cycles.
For example, the decimal representation of 1/3 is infinite, which means 0.33333 ..., where 3 will be repeated indefinitely. Similarly, the decimal representation of 1/7 is infinite, which means 0. 142857 142857 ..., where 142857 will be repeated indefinitely.
In mathematics, we can use the symbol of the upper horizontal line to represent the infinite cycle number. For example, 1/3 can be written as 0.3? 1/7 can be written as 0. 142857? . This horizontal line at the top represents the repeated parts.
Infinitely cyclic decimals cannot be accurately expressed as finite decimals or fractions. In calculation and mathematical applications, approximate values are usually used for processing.
Matters needing attention when using infinite cyclic decimal
1, precision: Infinite cycle decimal cannot be accurately expressed as finite decimal or fraction. When calculating or solving problems, we need to pay attention to the errors that may be introduced by this approximation.
2. Representation method: Generally, the upper horizontal line symbol can be used to represent the infinite loop part, such as 0.3? Represents 1/3. In addition, parentheses can also be used to indicate repeated parts, for example, 0. 142857( 142857) means 1/7.
3. Operation rules: When performing infinite cycle decimal operation, you need to follow the corresponding operation rules. For example, when adding, subtracting, multiplying and dividing two infinite cyclic decimals, it is necessary to align the cyclic parts according to the rules and perform operations.
4. Approximation: In actual calculation, in order to facilitate and reduce the error, the approximation of infinite cycle decimal is usually adopted. It can be truncated to a certain number of digits or replaced by approximation, but attention should be paid to the error introduced by approximation.