Integers include negative whole numbers, zero and positive whole numbers. A rational number can be written as ab, where a,b are integers and b 0. Its decimal terminates or repeats. An irrational number has a non-terminating, non-repeating decimal. Both families belong to the real numbers. **Number** | **Classification** -7 | Integer, rational, real 0.375= 38 | Rational, real 0. 3= 13 | Rational, real 2, pi | Irrational, real Example sqrt(49)=7 is rational even though it is written with a root sign. sqrt(50) is irrational because 50 is not a perfect square. A calculator display is finite: a displayed decimal approximation does not prove that the original number is rational.

Integers include negative whole numbers, zero and positive whole numbers. A rational number can be written as \(\dfrac ab\), where \(a,b\) are integers and \(b\ne0\). Its decimal terminates or repeats. An irrational number has a non-terminating, non-repeating decimal. Both families belong to the real numbers.

\(\sqrt{49}=7\) is rational even though it is written with a root sign. \(\sqrt{50}\) is irrational because \(50\) is not a perfect square.

A calculator display is finite: a displayed decimal approximation does not prove that the original number is rational.

Number	Classification
\(-7\)	Integer, rational, real
\(0.375=\dfrac38\)	Rational, real
\(0.\dot3=\dfrac13\)	Rational, real
\(\sqrt2\), \(\pi\)	Irrational, real

Number families and decimal forms

Number families and decimal forms