Rational Numbers-Full Definition (Kto12 G7-First Quarter)

Rational Numbers

A Rational Number is a real number that can be written as a simple fraction (i.e. as a ratio).

Most numbers we use in everyday life are Rational Numbers.

Example:

1.5 is a rational number because 1.5 = 3/2 (it can be written as a fraction)

Here are some more examples:

Number	As a Fraction	Rational?
5	5/1	Yes
1.75	7/4	Yes
.001	1/1000	Yes
-0.1	-1/10	Yes
0.111...	1/9	Yes
√2 (square root of 2)	?	NO !

Oops! The square root of 2 cannot be written as a simple fraction! And there are many more such numbers, and because they are not rational they are called Irrational.

Another famous irrational number is Pi (π):

Formal Definition of Rational Number

More formally we say:

A rational number is a number that can be in the form p/q
where p and q are integers and q is not equal to zero.

So, a rational number can be:

p

q

Where q is not zero

Examples:

p	q	p / q	=
1	1	1/1	1
1	2	1/2	0.5
55	100	55/100	0.55
1	1000	1/1000	0.001
253	10	253/10	25.3
7	0	7/0	No! "q" can't be zero!

Just remember: q can't be zero

Using Rational Numbers

If a rational number is still in the form "p/q" it can be a little difficult to use, so I have a special page on how to: Add, Subtract, Multiply and Divide Rational Numbers

Fun Facts ....

The ancient greek mathematician Pythagoras believed that all numbers were rational, but one of his students Hippasus proved (using geometry, it is thought) that you could not write the square root of 2 as a fraction, and so it was irrational.
But followers of Pythagoras could not accept the existence of irrational numbers, and it is said that Hippasus was drowned at sea as a punishment from the gods!