Non-zero rational numbers are numbers that can be expressed as a fraction, where the numerator and denominator are both integers, and the denominator is not zero. For example, the numbers 1/2, 3, and -4/5 are all non-zero rational numbers. They can be positive or negative, but they cannot equal zero. These numbers are part of the broader category of rational numbers, which includes all fractions and whole numbers. Non-zero rational numbers are important in mathematics because they can be used in various calculations and are essential for understanding concepts like proportions and ratios.