Maths Class 9 Chapter 1 Number System

# Maths Class 9 Chapter 1 Number System

Important Concepts and Formulas

1.      A number is called a rational number, if it can be written in the form p/q , where p, q  Z and q ≠ 0.

2.      A number is called an irrational number, if it cannot be written in the form p/q , where p, q  Z 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.      The collection of rational and irrational numbers is called 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 a rational number and s is an irrational number, then r + s, r – s, r × s and r/s are irrational numbers, r ≠ 0.

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

9.      To rationalize the denominator of 1/(+  b), we multiply this by (a – b) / (a – b), where a and b are integers.

10. Let a ˃ 0 be a real number and p and q be rational numbers, then

i.   ap.aq = ap + q                         ii.   (ap)q = apq
iii.  ap/aq = ap – q                      iv.  apbp = (ab)p