Word: Recurring Decimal
Definition: A recurring decimal is a type of decimal number in which a sequence of digits repeats infinitely. This means that after a certain point, the same group of numbers keeps appearing over and over again.
Usage Instructions: You can use the term "recurring decimal" when discussing numbers, especially in mathematics, to describe a decimal that doesn’t end but has a repeating pattern.
Example: - The number (0.333...) is a recurring decimal because the digit "3" repeats forever. We can also write it as (0.\overline{3}) to show that the "3" repeats. - Another example is (0.666...), which can be written as (0.\overline{6}).
Advanced Usage: In mathematics, recurring decimals are often discussed in relation to fractions. For instance, the fraction ( \frac{1}{3} ) equals the recurring decimal (0.333...). Understanding recurring decimals is important in topics involving limits and series.
Word Variants: - Non-recurring decimal: A decimal that has a finite number of digits and does not repeat (e.g., (0.25)). - Terminating decimal: A specific type of non-recurring decimal that ends after a certain number of digits (e.g., (0.75)).
Different Meaning: The term "recurring" can also be used outside of mathematics to refer to something that happens repeatedly over time, such as recurring meetings or recurring themes in literature.
Synonyms: There are not many direct synonyms for "recurring decimal," but you might refer to it as a "repeating decimal" which is commonly understood to mean the same thing.
Idioms and Phrasal Verbs: - While there are no idioms or phrasal verbs specifically related to "recurring decimal," you can use phrases like "come around again" to imply something that keeps happening, though it’s not mathematically specific.
Summary: A recurring decimal is a decimal number that has a repeating pattern of digits.