Real Number System

Real Numbers

Natural Numbers:  Positive numbers from 1 and up, with no decimal or fractional part.

1, 2, 3, 4, 5, …

Whole Numbers: Positive numbers with no decimal or fractional part, including 0.

01, 2, 3, 4, 5, …

Integers: All the numbers with no decimal or fractional part (positive or negative).

…-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, …

Rational numbers:  any number that can be expressed as the quotient or fraction p/q of two integers, (i.e. as a ratio). Since q may be equal to 1, every integer is a rational number.  q is a natural number (non-zero) denominator.

When we divide numerator between denominator of a fractional number, we can have two cases: A decimal with a finite number of digits. (terminating decimal), or a decimal that repeats over and over again indefinitely (repeating decimal).

1/2 can be represented as 0.5   (terminating decimal)

1/3 can be represented as 0.333333……. (repeating decimal)

A bar notation indicates that a number repeats forever. (repeating decimal)




Irrational numbers: any number that cannot be exactly expressed as a ratio of two integers.

Real Numbers: All the numbers that can be represented on a number line.






The Real Number System