Irrational numbers are numbers that cannot be written as a fraction with the numerator and denominator as integers. This means that any number that is not a terminating decimal number or a repeating decimal number is irrational. Examples of irrational numbers are:
2
,
3
,
4
3
,
π
,
1
+
5
2
≈
1
,
618
033
989
2
,
3
,
4
3
,
π
,
1
+
5
2
≈
1
,
618
033
989
(1)When irrational numbers are written in decimal form, they go on forever and
there is no repeated pattern of digits.
If you are asked to identify whether a number is rational or irrational, first write the number in decimal form. If the number is terminated then it is rational. If it goes on forever, then look for a repeated pattern of digits. If there is no repeated pattern, then the number is irrational.
When you write irrational numbers in decimal form, you may (if you have a lot of time and paper!) continue writing them for many, many decimal places. However, this is not convenient and it is often necessary to round off.
Which of the following cannot be
written as a rational number?
Remember: A rational number is a fraction with numerator and denominator as integers. Terminating decimal numbers or repeating decimal numbers are rational.

π
=
3
,
14159265358979323846264338327950288419716939937510
...
π
=
3
,
14159265358979323846264338327950288419716939937510
...
 1,41,4

1
,
618
033
989
...
1
,
618
033
989
...
 100100