Rational Numbers

A Rational Number can exist made by dividing an integer by an integer.
(An integer itself has no fractional part.)

Example:

i.5 is a rational number because 1.5 = 3/ii   (3 and 2 are both integers)

Rational Number

Most numbers we use in everyday life are Rational Numbers.

You can make a few rational numbers yourself using the sliders beneath:

numbers/images/rational.js

Here are some more examples:

Number Equally a Fraction Rational?
5 5/1 Yep
ane.75 vii/4 Yep
thousand 1000/1 Yes
.001 i/1000 Yes
−0.1 −ane/ten Yes
0.111... ane/ix Yep
√2
(foursquare root of ii)		 ? NO !

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

Another famous irrational number is Pi (π):

Rational Number

Formal Definition of Rational Number

More than formally nosotros say:

A rational number is a number that tin be in the course p/q
where p and q are integers and q is non equal to nothing.

And then, a rational number can be:

p q

where q is not zero.

Examples:

p q p / q =
one ane 1/ane ane
1 ii 1/2 0.five
55 100 55/100 0.55
ane 1000 1/thou 0.001
253 10 253/10 25.iii
7 0 7/0 No! "q" tin't exist null!

Simply remember: q tin't be zero.

Using Rational Numbers

Fun Facts ....

The ancient greek mathematician Pythagoras believed that all numbers were rational, just ane of his students Hippasus proved (using geometry, it is thought) that you could non write the square root of two as a fraction, and and then it was irrational.

But followers of Pythagoras could non accept the beingness of irrational numbers, and it is said that Hippasus was drowned at sea as a punishment from the gods!

1667, 1668, 3984, 3983, 5347, 9002, 9072, 9000, 9001, 9071