Ratsionaalarvu

Ratsionaalarvu (rational numbers) are numbers that can be expressed as a ratio a/b of two integers, with b nonzero. They can be written as p/q in reduced form, where p and q are integers and gcd(p,q) = 1. In such a form, the sign is carried by p and q is positive. Every rational number has a decimal expansion that either terminates or becomes periodic, repeating a block of digits. For example, 3/4 = 0.75 terminates, while 1/3 = 0.333... repeats. Every integer is a rational number, since n = n/1.

Ratsionaalarvu form the set Q, which is closed under addition, subtraction, multiplication, and division by a nonzero rational. In other words, the sum, difference, product, or quotient (where the divisor is not zero) of two rationals is again rational. The rationals are dense in the real numbers: between any two real numbers there exists a rational number. They form a countable set and constitute a field, meaning they satisfy the usual arithmetic laws and have multiplicative inverses for nonzero elements.

Relation to other numbers: numbers that cannot be expressed as a ratio of integers are irrational (examples include sqrt(2) and pi). Rational numbers are used to model fractions, ratios, and precise measurements, and they underpin much of elementary algebra and number theory.