Definition:
An irrational number is a number that cannot be expressed as a simple fraction or a ratio of two integers. In contrast, a rational number is a number that can be expressed as a ratio of two integers.

Characteristics of Rational Numbers:
- Rational numbers can be expressed as fractions.
- They can be written in the form a/b, where a and b are integers and b is not equal to zero.
- Rational numbers either terminate or repeat when expressed as decimals.
- Examples of rational numbers include 1/2, 3/4, and -5.

Characteristics of Irrational Numbers:
- Irrational numbers cannot be expressed as fractions.
- They have non-repeating and non-terminating decimal expansions.
- Examples of irrational numbers include √2, π, and e.
- Irrational numbers are often represented by symbols or as decimals that do not repeat or terminate.

Distinguishing Factors:
- The key difference between rational and irrational numbers lies in their representation. Rational numbers can be written as simple fractions, while irrational numbers cannot.
- Another distinguishing factor is the decimal representation of these numbers. Rational numbers either terminate or repeat, whereas irrational numbers have non-repeating and non-terminating decimals.
In conclusion, the distinction between rational and irrational numbers lies in their representation as fractions and decimals. Rational numbers can be expressed as simple fractions, while irrational numbers cannot and have non-repeating and non-terminating decimal expansions.