## Rational and Irrational Numbers

A rational number is any number that can be written as a fraction, one whole number divided by another.

are all rational.

Many decimals are rational too. If they only have so many decimal places then they are rational because they be written as something over 1 followed by some zeroes. For example 0.9786 is rational becauseAny number with a decimal expansion that repeats is also rational because for example

We can write the shortest repeating fraction as that number divided by a number made up of so many nines. The number of nines is equal to the length of the pattern.

There are however, many examples of irrational numbers.

are all irrational.

There are also simple rules to make more rational and irrational numbers

or

No such similar rules exist for the sums, products or quotients of irrational numbers. They may be rational or irrational.

For exampleandare both irrational butwhich is rational

andare both irrational but

andBoth of these examples return rational numbers.