What makes a number rational?

Answer 1

A rational number is one that can be expressed as ratio(or fraction) of two integers: given integers a & b (with b ≠ 0), then the fraction a / b (or a ÷ b) will be a rational number. We need to specify that b not equal to zero, as division by zero is not defined (well not for most math applications).

So Irrational Numbers such as pi, e, and square root of 2: cannot in any way be resolved into a fraction of two integers. All rational numbers can. Examples are:

• 0 is rational, let a = 0, b = 1, or any other non-zero integer: 0/1 = 0
• Whole numbers are rational: 1/1 = 1; 2/1 = 2; 100/25 = 4, etc.
• Negative integers are also rational: (-4)/(2) = -2, or (20)/(-5) = -4
• All fractions (proper and improper) which have integers in the numerator, and non-zero integer in denominator, as well as mixed numbers are rational {positive and negative} will be rational numbers.

Answer 2

All whole numbers and fractions are rational numbers because irrational numbers can't be expressed as whole numbers or fractions.