Question

27
NUMBER SYSTEMS
1.7 Summary
In this chapter, you have studied the following points:
9
1. A number r is called a rational number, if it can be written in the form ?, where p and q are
integers and q *0.
9.
2. A numbers is called a irrational number, if it cannot be written in the form ?, 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 real number corresponding to every point on the number line. Also, corresponding
to each point on the number line, there is a real number.
r
are
7. If ris rational and sis irrational, then r+s andrs are irrational numbers, and rs and
S
irrational numbers, r=0.
а
VT
8. For positive real numbers a and b, the following identities hold:
(1) Vab=ado
ſa
b
(ii) (Va + vb) (Va - Vb) = a - b (iv) (a + vb) (a -vá) = a’ - b
(v) (Ta + vb) =a + 2ab + b
1
ſa-b
9. To rationalise the denominator of
-, where a and bare
we multiply this by
Sa+b
Ja - b
integers.
10. Let a > 0 be a real number and p and q be rational numbers. Then
(i) apa? = a +9
(ii) (a)' = apa
a
a²-9
(iv) ab? = (aby
a!​

Answer 1

Answer:

1. p/q. q≠0

2. p/q

Hope my answers are helpful