circulating decimal
/'sə:kjuleitiɳ'desiməl/
Definition
Noun: A circulating decimal is a decimal number in which a digit or a sequence of digits repeats infinitely without end. This is also commonly known as a repeating decimal.
Usage
The term is used in mathematics to describe the decimal representation of a rational number that is not terminating. The repeating sequence is often indicated by placing a bar (vinculum) over the repeating digits. - The fraction 1/3 is expressed as the circulating decimal 0.333... - When you convert 2/7 to a decimal, you get a circulating decimal.
Examples
Advanced Usage
- Indicating Repeating Digits: In formal notation, a circulating decimal is written by placing a dot over the first and last digit of the repeating block, or a bar over the entire repeating sequence. For example, 0.3̅ or 0.̄3 for 0.333...
- Conversion from Fractions: A circulating decimal results when a fraction, in its simplest form, has a denominator with prime factors other than 2 or 5.
Variants and Related Words
- Repeating Decimal: The more common modern synonym for circulating decimal.
- Recurring Decimal: Another exact synonym, frequently used in British English.
- Non-terminating Decimal: A broader category that includes both repeating and non-repeating (irrational) decimals.
Synonyms
- Repeating Decimal
- Recurring Decimal
- Periodic Decimal
Antonyms
- Terminating Decimal (a decimal that ends after a finite number of digits)
Related Phrases/Concepts
- Vinculum: The horizontal bar placed over the repeating digits in a circulating decimal.
- Rational Number: Any number that can be expressed as a fraction of two integers, which will have a decimal expansion that is either terminating or a circulating decimal.
Noun
-
a decimal with a sequence of digits that repeats itself indefinitely
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