periodic decimal: meaning, definition, pronunciation and examples
LowTechnical, Academic
Quick answer
What does “periodic decimal” mean?
A decimal fraction in which a digit or group of digits repeats infinitely, also known as a repeating or recurring decimal.
Audio
Pronunciation
Definition
Meaning and Definition
A decimal fraction in which a digit or group of digits repeats infinitely, also known as a repeating or recurring decimal.
In mathematics, a representation of a rational number where, after a certain point, the decimal expansion becomes an infinitely repeating sequence of one or more digits. The repeating sequence is called the repetend or period.
Dialectal Variation
British vs American Usage
Differences
In British English, 'recurring decimal' is the most common term. 'Periodic decimal' is understood but less frequent. In American English, 'repeating decimal' is predominant, with 'periodic decimal' being a formal alternative.
Connotations
All variants are neutral and purely descriptive. 'Periodic decimal' may sound slightly more formal or academic.
Frequency
In both dialects, 'periodic decimal' is less common in everyday educational contexts than the regional preferred terms ('recurring' in UK, 'repeating' in US).
Grammar
How to Use “periodic decimal” in a Sentence
[Number] is a periodic decimal.The fraction yields a periodic decimal.One can denote the periodic decimal with a bar.Vocabulary
Collocations
Examples
Examples of “periodic decimal” in a Sentence
adverb
British English
- The digits recur periodically in the quotient.
American English
- The sequence repeats periodically after the third place.
adjective
British English
- The decimal expansion was found to be periodic.
- We studied periodic decimal representations.
American English
- The result is a periodic decimal number.
- He explained the periodic decimal pattern.
Usage
Meaning in Context
Business
Virtually never used.
Academic
Used in mathematics textbooks, papers, and lectures, especially in number theory and foundational arithmetic.
Everyday
Rare, except when helping with school mathematics homework.
Technical
Used in precise mathematical discourse, computer algebra systems, and educational software.
Vocabulary
Synonyms of “periodic decimal”
Strong
Weak
Vocabulary
Antonyms of “periodic decimal”
Watch out
Common Mistakes When Using “periodic decimal”
- Pronouncing 'periodic' as /ˈpɪəriədɪk/ (like 'period' + 'ic') instead of the correct /ˌpɪəriˈɒdɪk/ (stress on 'od').
- Writing 'periodical decimal'.
- Confusing it with a 'terminating decimal'.
FAQ
Frequently Asked Questions
Yes. By definition, a number is rational if and only if its decimal expansion is either terminating or periodic.
A pure periodic decimal begins its repetend immediately after the decimal point (e.g., 0.333...). A mixed (or eventually) periodic decimal has non-repeating digits before the repetend begins (e.g., 0.1666...).
Let x equal the decimal. Multiply x by 10^n where n is the length of the period, subtract the original x, and solve the resulting equation for x as a fraction in its simplest form.
Not necessarily. The term encompasses both pure (immediate) and mixed (eventual) repetition. The key feature is the eventual infinite repetition of a fixed block of digits.
A decimal fraction in which a digit or group of digits repeats infinitely, also known as a repeating or recurring decimal.
Periodic decimal is usually technical, academic in register.
Periodic decimal: in British English it is pronounced /ˌpɪəriˈɒdɪk ˈdɛsɪml/, and in American English it is pronounced /ˌpɪriˈɑːdɪk ˈdɛsəməl/. Tap the audio buttons above to hear it.
Phrases
Idioms & Phrases
- “It's a periodic decimal – it goes on forever.”
- “The numbers repeat in a periodic fashion.”
Learning
Memory Aids
Mnemonic
Think of a period in a sentence that repeats itself. A PERIODic decimal has a repeating group of digits after the decimal point.
Conceptual Metaphor
A decimal number caught in an infinite loop.
Practice
Quiz
Which notation is commonly used to indicate the repetend in a periodic decimal?