# What have we discussed

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In this chapter, you have studied the following points:

- A number
**r**is called anumber, if it can be written in the form , where p and q are integers and q ≠ 0.p q

2. A number **s** is called a

3. 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

4. The decimal expansion of an irrational number is non-terminating non-recurring. Moreover, a number whose decimal expansion is non-terminating non-recurring is

5. All the rational and irrational numbers make up the collection of

6. If **r** is rational and **s** is irrational, then **r** + **s** and **r** – **s** are irrational numbers, and rs and

7. For positive real numbers a and b, the following identities hold: Let a and b be positive real numbers. Then

(i)

(ii)

(iii)

(iv)

(v)

8. To rationalise the denominator of

9. Let a > 0 be a real number and p and q be rational numbers. Then

(i) | (ii) |

(iii) | (iv) |