The numbers in mathematics can be classified into different types. It is done so that we can easily identify and make sense of them. All the numbers below are real numbers. They are found on the number line. The two main categories of the real numbers are rational and irrational numbers. The rational numbers are further subdivided into natural numbers, whole numbers, and integers.

**Natural or Counting Numbers** - The set of natural or counting numbers are the numbers that we use to count which start with the number \(1\). The numbers in this set don't contain fractional parts or decimal points.

$$1,2,3,4,...$$

**Whole Numbers** - The set of whole numbers is simply the set of the natural numbers plus the number zero \(0\) attached to it.

$$0,1,2,3,4,...$$

**Integers** - The set of integers is the combination of the set of the whole numbers and the negative natural numbers.

$$...,-4,-3,-2,-1,0,1,2,3,4,...$$

**Rational Numbers** - Rational numbers are numbers that can be written as a ratio of integers. A ratio of two integers can simply be pictured as a fraction. However, the denominator of the fraction cannot be equal to zero.

$${a \over b}$$

where \(a\) and \(b\) are integers but \(b \ne 0\)

Examples: \({2 \over 7}\), \({-1 \over 5}\)

Rational numbers can be written in decimal form. A decimal number is a rational number if the decimal part terminates or it repeats indefinitely.

Decimal numbers that terminate:

\(0.25\)

\(3.17\)

Decimal numbers that repeat indefinitely:

\(0.5555...\)

\(0.131313...\)

**Irrational Numbers **- Irrational numbers are numbers that cannot be written as fractions. Or when written in decimal form, they do not terminate, and more importantly, they do not repeat.

Examples: \(\sqrt 2 \), \(\pi \)