Rational numbers

• A rational number is a number that can be expressed as a fraction p/q of two integers, a numerator p and a non-zero denominator q.

• Since q may be equal to 1, every integer is a rational number.

• The set of all rational numbers is denoted by ℚ (quotient).

• The decimal expansion of a rational number either:

  • terminates after a finite number of digits

  • infinitely repeats a particular finite sequence of digits

• Rationals may be build from the natural numbers by including a multiplicative inverse, 1/n, for each nonzero integer n, along with the products formed by multiplying these inverses with integers.