Question

CLASS 9TH CBSE MATH CHAPTR1 NUMBER SYSTEM SUMMARY...​

Answer 1

Answer:

A number r is called a rational number if it can be written in the form $\frac{p}{q}$

, where p and q are  integers and q ≠ 0.

2. A number s is called an irrational number if it cannot be written in the form $\frac{p}{q}$, where p and

q are integers and q ≠ 0.

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 rational.

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 irrational.

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

6. 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.

7. If r is rational and s is irrational, then r + s and r – s are irrational numbers, and rs and  $\frac{r}{s}$   are

irrational numbers, r ≠ 0.

8. For positive real numbers a and b, the following identities hold:

(i) √ab=√a+√b

(iii)(√a+√b)(√a-√b)=a-b

(√a+√b)²=a+2√ab+b

9. To rationalise the denominator of  1/(√a+b) we multiply it by (√a-b)/(√a-b)

where a and b are

integers