Rational Numbers Definition:
A number that can be expressed as
a fraction p/q of two Integers,
a numerator p
and a non-zero denominator q.
Rational Numbers Notation
We write Rational Numbers as ℚRational Numbers extend from but do not include (-∞, ∞)
What do Rational Numbers Include?
Natural (Counting) Numbers (ℕ) (1, 2, 3, 4, ...).Since every natural number
can be written as itself divided by 1
Whole Numbers (0, 1, 2, 3, 4, ...)
Since every whole number can be written as itself divided by 1
Negative Counting Numbers (..., -4, -3, -2, -1)
Since every negative counting number
can be written as itself divided by 1
Fractions (3/5, -4/7)
Decimals (2.4, -8.1)
What do Rational Numbers NOT Include?
Positive Infinity ∞Negative Infinity -∞
Imaginary Numbers like i = √-1
Properties of Rational Numbers
Positive Rational Numbers areto the right of 0 on a number line
Negative Rational Numbers are
to the left of 0 on a number line
As we move right on the number line,
Rational Numbers increase in value
As we move left on the number line,
Rational Numbers decrease in value
Extend infinitely (but do not include infinity)
Any non-zero Rational Numbers is either negative or positive.
