Summary

Videos

References

A number which can be written in the form $\frac{\text{a}}{\text{b}}$ where

Rational numbers are of two types depending on whether their decimal form is terminating or recurring.

A number which cannot be written in the form $\frac{\text{a}}{\text{b}}$, where *a* and *b* are integers and b ≠ 0 is called a irrational number. Irrational numbers which have non-terminating and non-repeating decimal representation.

The sum or difference of a two irrational numbers is also rational or an irrational number.

The sum or difference of a rational and an irrational number is also an irrational number.

Product of a rational and an irrational number is also an irrational number.

Product of a two irrational numbers is also rational or an irrational number.

Let p be a prime number. If p divides a

If $\frac{\text{p}}{\text{q}}$ is a rational number, such that the prime factorisation of q is of the form 2

If a rational number is a terminating decimal, it can be written in the form $\frac{\text{p}}{\text{q}}$ , where p and q are co prime and the prime factorisation of q is of the form 2

If $\frac{\text{p}}{\text{q}}$ is a rational number such that the prime factorisation of q is not of the form 2

A number which can be written in the form $\frac{\text{a}}{\text{b}}$ where

Rational numbers are of two types depending on whether their decimal form is terminating or recurring.

A number which cannot be written in the form $\frac{\text{a}}{\text{b}}$, where *a* and *b* are integers and b ≠ 0 is called a irrational number. Irrational numbers which have non-terminating and non-repeating decimal representation.

The sum or difference of a two irrational numbers is also rational or an irrational number.

The sum or difference of a rational and an irrational number is also an irrational number.

Product of a rational and an irrational number is also an irrational number.

Product of a two irrational numbers is also rational or an irrational number.

Let p be a prime number. If p divides a

If $\frac{\text{p}}{\text{q}}$ is a rational number, such that the prime factorisation of q is of the form 2

If a rational number is a terminating decimal, it can be written in the form $\frac{\text{p}}{\text{q}}$ , where p and q are co prime and the prime factorisation of q is of the form 2

If $\frac{\text{p}}{\text{q}}$ is a rational number such that the prime factorisation of q is not of the form 2