repeating decimal
Definition
Noun: A repeating decimal is a decimal representation of a rational number where, after a certain point, a specific digit or sequence of digits repeats infinitely without end. This repeating sequence is often indicated by a bar placed over the repeating digits.
Usage
The term is used in mathematics to describe the decimal form of fractions that do not result in a terminating decimal. It is a precise way to express numbers that have an infinite but repeating pattern.
Examples
- The fraction 1/3 is equal to the repeating decimal 0.333..., which can be written as 0.3̄.
- When you convert 2/7 to a decimal, you get the repeating decimal 0.285714285714...
- A number like 0.166666... is a repeating decimal where the digit "6" repeats indefinitely.
Advanced Usage
- Period: The repeating sequence of digits in a repeating decimal is called its . For example, in 0.142857142857..., the period is "142857".
- Terminating vs. Repeating: A decimal that ends (e.g., 0.5) is a . A decimal with an infinitely repeating pattern is a (also called a ).
Variants and Related Words
- Recurring Decimal: This is a direct synonym for "repeating decimal" and is commonly used, especially in British English.
- Non-terminating Decimal: A broader term for any decimal that does not end, which includes both repeating and non-repeating (irrational) decimals.
Synonyms
- Recurring decimal
- Periodic decimal
Related Concepts (Not Phrasal Verbs/Idioms)
- Rational Number: A number that can be expressed as a fraction of two integers. All repeating decimals represent rational numbers.
- Vinculum: The horizontal bar ( ¯ ) placed over digits to indicate they repeat.
- Ellipsis: The three dots (...) used informally to indicate the repetition continues infinitely.
Noun
-
a decimal with a sequence of digits that repeats itself indefinitely
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