Rational numbers can be expressed as fractions where the numerator and denominator are integers and the denominator is not zero. They were studied by classical Greek and Indian mathematicians as part of number theory. Rational numbers are needed for measurement and describing quantities that cannot be adequately described by integers alone. Early fractions represented reciprocals of integers, and Egyptians used Egyptian fractions around 1000 BC to divide quantities. The modern notation for fractions using a horizontal bar was introduced by Arabs.