Rational and irrational number help. What is a rational number?

A rational number is a number that can be written as a fraction, whereas an irrational number is a number that cannot be written as a fraction.

So a rational number can be written in the form a/b where a and b are whole numbers.

To decide whether or not a number is rational, just try to write your number as a fraction – this might not be obvious at first, but you will find many different types of numbers can written down as a fraction.

Example 1

Is 3/7 a rational or irrational number?

3/7 is obviously rational as it already is a fraction.

Example 2

Is 0.67 rational or irrational?

Yes because 0.67 = 67/100.

Example 3

Is √9 rational or irrational?

Yes because √9 = 3, and 3 can be written as 3/1 (all whole numbers are rational).

Example 4

Is 3π rational or irrational?

3π is irrational as Pi is a non terminating decimal, therefore it cannot be written as a fraction.

Any multiple of Pi cannot be written as fraction.

Example 5

Is √7 rational or irrational?

√7 is irrational the square root of 7 is 2.6457... and again this is a non terminating decimal.

Most roots are irrational numbers, except when you are rooting a square root like in example 3.

Example 6

Is 0.3r a rational or irrational number?

0.3r is a recurring decimal, and can be written as 1/3. Therefore, 3r is rational.

Summary

A rational number is any number that can be written as a fraction. An irrational number cannot be written as a fraction.

The majority of numbers with a Pi or a square root in them will be irrational numbers.

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