The difference between Rational number and Real number
When used as nouns, rational number means a number that can be expressed as the ratio of two integers, whereas real number means the limit of a convergent sequence of rational numbers, whether the limit is a rational number such as 2, -5, or 2/7 or whether the limit is an irrational number such as the square root of two or the circumference of the circle whose radius is one.
check bellow for the other definitions of Rational number and Real number
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Rational number as a noun (mathematics):
A number that can be expressed as the ratio of two integers.
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Real number as a noun (mathematics):
The limit of a convergent sequence of rational numbers, whether the limit is a rational number such as 2, -5, or 2/7 or whether the limit is an irrational number such as the square root of two or the circumference of the circle whose radius is one.
Examples:
"Every integer is a real number, but not vice versa."
"A [[real number]] can be regarded abstractly as an equivalence class of Cauchy sequences of real numbers.''<sup>w P-adic_number#Analytic_approach WP</sup>"
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Real number as a noun (computing):
A floating-point number.
Examples:
"Even if you pass <tt>sqrt</tt> an integer, it returns a [[real number]]."