What is the difference between rational numbers and whole numbers?

Answer 1

A whole number is usually defined as any non-negative integer (0, 1, 2, 3, ....). However, some limit the definition to all positive integers (1, 2, 3, ...), and others de-limit it to include all integers, whether positive, negative, or zero (... -2, -1, 0, 1, 2, ...). A rational number is any number that can be expressed as a ratio of two integers. Obviously, all integers are rational numbers because an integer can be expressed as a ratio of itself and 1 (i.e., 7 = 7/1). Also, all fractions in which both the enumerator and denominator are integers are rational numbers (that follows from the definition). But also, any decimal number that has a finite number of decimal places can be expressed as a ratio (4.5632674 = 45632674/10000000). Furthermore, any decimal number with an infinite number of decimal places, as long as they repeat, can be expressed as a ratio (0.333333... = 1/3). Basically, the only numbers that are not a rational numbers are those numbers for which both 1) there are an infinite number of decimal places, and 2) the digits in the decimal places never repeat themselves. Note that, when it is said that the decimal places "repeat", it need not be a single digit repeated infinitely. It could be a series of digits repeated infinitely. For example, 1/7 = 0.142857142857142857142857..., with the series "142857" repeated infinitely. Note also that, though not included in the examples above, negative numbers can be rational numbers (-7, -1/3, -4.5632674, and -0.142857142857142857142857... are all rational). In fact, any positive rational number can be made negative (and still remain rational), by multiplying it by -1. A number that is not rational is referred to as an "irrational number". Commonly seen examples include pi (3.14159262...), e (2.71828182845), and the square root of 2. Both rational and Irrational Numbers are part of the set of numbers referred to as "real numbers". This set encompasses all numbers that actually exist, from negative infinity to positive infinity, and every point in between.