Word: Continued Fraction
Part of Speech: Noun
Simple Definition: A continued fraction is a special way to write a number as a fraction. It starts with an integer (a whole number) and then adds more fractions to it in a specific pattern.
How It Works: You can think of a continued fraction like this:
Example: - The continued fraction for the number 2.5 can be written as: - 2 + 1/(2 + 1/(2 + ...))
This means you start with 2, then add a fraction that involves 2 again, and this can keep going.
Advanced Usage: Continued fractions are used in mathematics, especially in number theory and for approximating real numbers. They can represent irrational numbers and are useful for finding the best rational approximations of numbers.
Word Variants: - There are no direct variants of "continued fraction," but you might encounter related terms such as "simple continued fraction," which is a specific type of continued fraction where each fraction has an integer in the denominator.
Different Meanings: The term "fraction" on its own refers to a part of a whole or a division of numbers, but "continued fraction" has a specific mathematical context.
Synonyms: There are no direct synonyms for "continued fraction," but you might refer to it as a "recursive fraction" in some contexts due to its repeating nature.
Idioms and Phrasal Verbs: There are no idioms or phrasal verbs specifically related to "continued fraction," as it is a technical term primarily used in mathematics.
Summary: A continued fraction is a unique and complex way to express numbers that involves a series of fractions where each fraction builds on the previous one.