The natural numbers are the positive integers and zero. Rational numbers are ratios of integers. Irrational numbers have decimal digits dn
that do not repeat. Thus the repeating decimals 1/2 = 0.50000 . . . and are rational, while π = 3.141592654 . . . is irrational. Decimal arithmetic was invented in India over 1500 years ago but was not widely adopted in the Europe until the seventeenth century.