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If a number can be expressed as a ratio of two whole numbers then it's rational.
Alternatively, if a number can be expressed in decimal with a finite number of digits or as a repeating decimal then it's rational.

All integers are rational numbers. The easiest way to see that is to write an integer as a fraction with 1 as a denominator; 4=4/1=8/2; 5=5/1.
Any number that can be written as a ratio of two integers numbers is by definition a rational number ( it is a ratio---rational).
Any decimal number with a periodic decimal part can be cast as a fraction, so it is rational.
An irrational number is a number that cannot be written as a fraction.
Examples: PI, sqRT(2), Sqrt(3), SQRT(5), e. There is an infinite number of them.

The product of two rational numbers is another rational number.

The opposite of any number (be it integer, rational, or real) is the same number preceded by the negative sign.
Example : the opposite of a is -a (read it a negative a)
opposite of (-b) is -(-b)=b
A rational number is a number that can be written as a fraction. You should note that the set of rational numbers contains the set of all integers .
The opposite of 15/37 is -(15/37) which is equivalent to (-15)/37 and 15/(-37).

The opposite of any number (be it integer, rational, or real) is the same number preceded by the negative sign.
Example : the opposite of a is -a (read it a negative a)
opposite of (-b) is -(-b)=b
A rational number is a number that can be written as a fraction. You should note that the set of rational numbers contains the set of all integers .
The opposite of 15/37 is -(15/37) which is equivalent to (-15)/37 and 15/(-37).

A rational number that can written as the RATIO of two whole numbers.
Examples:
1. Any whole number (-1, +13, -57) because they can be written as -1/1, 13/1 , -57/1.
2.Any number of the form a/b where a and be are integers (whole numbers) 1/3 , 17/(-9), 27/11, -17/9
13.572 572 572... where the sequence 572 (called the period) repeats for ever
-29.0123478478 478...
Numbers such as the square roots of numbers that are not perfect squares are not rational. They are irrational numbers. SQRT(2), SQRT(5), SQRT(6), SQRT(7), SQRT(8), SQRT(10), PI, e the base of natural logarithm, sin(22 degrees), cos(58),

A rational number is a number that can be expressed as the RATIO (see rational) of two integer (whole) numbers. 8 is an integer, and so is 3. The number 8/3 is a RATIO of two integers :it fits the definition of a rational number.

There are an infinite number of rational numbers between any two distinct rational numbers.

There are an infinite number of rational numbers between any two rational numbers.

Given any two rational numbers, the number midway between them is also rational. By the same logic, the number midway between the smaller of the two original numbers and the midpoint is also rational. And so is the number midway between the first number and the second midpoint. And so is the number midway between the first number and third midpoint... and so on.

You're looking for a website with examples of rational and irrational numbers? Here's an extensive one:

1. Rational: Link
2. Irrational: Link

Or are you just asking for a few examples?

1. Rational: 5, 2/4, -34
   
2. Irrational: ?2, ?

Hope this helps!