# NCERT Chapter Summary: Number Systems

A number r is called a **rational number**, if it can be written in the form p/q, where p and q are integers and q ≠ 0. A number s is called a **irrational number**, if it cannot be written in the form p/q, where p and q are integers and q ≠ 0.

The **decimal expansion** of a rational number is either terminating or non-terminating recurring. Moreover, a number whose decimal expansion is terminating or non-terminating recurring is rational. The decimal expansion of an irrational number is non-terminating non-recurring. Moreover, a number whose decimal expansion is non-terminating non-recurring is irrational.

All the rational and irrational numbers make up the collection of **real numbers**. There is a unique real number corresponding to every point on the number line. Also, corresponding to each real number, there is a unique point on the number line.

If r is rational and s is irrational, then r + s and r - s are irrational numbers, and rs and r/s are irrational numbers, r ≠ 0.

To rationalise the denominator of 1/(√a + b), multiply this by (√a - b)/(√a - b) where a and b are integers.