Download 8.Rational Numbers

RATIONAL NUMBERS
1.
If x and y are two rational numbers, which of the following are true:
(i)
x + y is a rational number
(ii) x – y is a rational number
(iii) xy is a rational number
(iv) x/y is a rational number
2. Insert five rational numbers between
3
2
and
5
3
-2
-1
and
5
5
0 and 0.1
(i)
(ii)
(iii)
3. Show the following are not rational numbers
(i)
5
(ii)
3
6
(iii)
3
7
4. Represent the following on the number line:
3
8
5
(ii) -1
7
(iii)
5
(i)
2
(iv) 1.15
5. Define
(a) Rational numbers
(b) Irrational numbers
Give an example of each.
6. Which of the following are rational numbers and which are irrational numbers:
3,
7.
6, π,
3
9,
3
16
State whether true of false. In each case give one more example.
(i) As
2 is irrational, so - 2 will also be irrational
(ii) Sum of a rational and irrational numbers is always irrational, example
2 + 3, − 5 − 12
(iii) Product of a non zero rational number and an irrational number can
sometimes be rational.
(iv) Sum of two irrational numbers need not be irrational
(v) Product of two irrational numbers need not be irrational
8. Give reasons and say which of the following are rational or irrational.
(i) − 5
(ii) 2 + 6
(iii)
7 − 2 (iv)
7
3
5
(v)
(3 + 3 )
9. Find two rational and two irrational numbers
(a) between 0.15 and 0.16
(b) between
2 and
3
10. What is the absolute value of a number x defined as ?
2
11. Solve the following:-
(i) −5 + 3
(ii) −2 − 7
(iii) −2−−5
(iv) 2 −5 − 9
12. Solve the equations
(i) x + 2= 5
(ii) 3 − 5x= 12
(iii) 3x +x= − 12
(iv) 5x+ x = 12
13. Find the real numbers on real line satisfying the equation
<x< 2