RATIONALS Meaning and
Definition
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Rationals, in mathematics, refer to a subset of the real numbers that can be expressed as a ratio or fraction of two integers. The term "rational" is derived from the Latin word "ratio," which means "ratio," highlighting the key characteristic of these numbers being expressible as a ratio of two whole numbers.
In more precise terms, a rational number is any number that can be written in the form p/q, where p and q are integers and q is not equal to zero. For example, 1/2, -5/3, and 4/1 are all rational numbers. Importantly, the set of rationals includes both positive and negative fractions, as well as whole numbers, since any whole number can be expressed as a fraction with a denominator of 1.
Rationals possess certain fundamental properties. They can be ordered on a number line, allowing for comparisons of magnitude. Additionally, they can be added, subtracted, multiplied, and divided using arithmetic operations, resulting in another rational number. However, it is essential to note that not all real numbers are rational. For instance, the square root of 2, pi, and Euler's number (e) are all examples of irrational numbers that cannot be expressed as a fraction. These irrational numbers exist alongside the rational numbers and together complete the real number system, forming a continuum of values on the number line.
Common Misspellings for RATIONALS
Etymology of RATIONALS
The word "rationals" is derived from the Latin word "rationalis", which comes from the Latin term "ratio" meaning "reason". In Latin, the term "rationalis" was used to describe things relating to reason or logic. In mathematics, the word "rationals" refers to the set of rational numbers, which are numbers that can be expressed as a ratio of two integers, hence the term.
