1. Rational numbers, denoted by $Q$, are numbers that can be expressed as the ratio of two integers $\frac{a}{b}$, where the denominator b is not zero.

2. Rational numbers includes natural numbers, whole numbers, integers, fractions, and both terminating and repeating decimals.

3. A rational number $x = \frac{a}{b} \in Q$ is classified as:

– A proper fraction if $( a < b)$.

– An improper fraction if $( a \geq b)$.

– A mixed fraction if it is expressed as $y = c\frac{a}{b}$, where $ c $ is an integer and $( \frac{a}{b} )$ is a proper fraction.

4. If $\frac{a}{b}$​ is in its simplest form, where a and b are relatively prime (i.e., their greatest common factor, GCF(a, b), is 1)

5. Rational numbers can also be represented by either terminating or repeating decimals.

• A terminating decimal is one with a finite number of digits, and it can be converted to a fraction with a denominator that is a power of 10.
• A repeating decimal has digits that repeat infinitely and can be converted to a fraction using a method involving setting up an equation to isolate the repeating part.

6. Representation on the Number Line:

   – Rational numbers like \( -2 \), \( 3 \), \( \frac{3}{5} \), and \( -\frac{7}{6} \) can be located by converting them to decimal form first.

This summary encapsulates the basic principles of rational numbers, their classifications, and conversions between fractions and decimals, as well as their representation on a number line.