Download Assignment Rational and Irrational Numbers

Assignment
Rational and Irrational Numbers
1. (a) Express 0.6 in the form
p
.
q
(b) Express 15.75 as a fraction in its lowest terms.
(c) Find the decimal representation of
8
.
3
2. (a) Without actual division find out which of the following fractions
are terminating decimals.
(i)
15
9
(ii)
21
20
(iii)
7
8
(b) Express 0.32 as a vulgar fraction.
(c) Express
22
as a decimal correct to four decimal places.
7
3. (a) Insert a rational number between
1
1
and .
3
2
(b) Which of the following are rational numbers ?
(i)
(c) Show that
(ii)
22
7
(iii) 3.14
2 is not a rational number.
4. (a) Give an example of two irrational numbers, the product of which is
(i) a rational number
(b) Identify
(ii) an irrational number
45 as rational number or irrational number.
(c) Insert a rational and an irrational number between 2 and 3.
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Assignment
5. (a) Prove that
3 – 2 is an irrational number.
(b) Show that 3 – 3
(c) Simplify
3
2
3 + 3 is a rational number.
by rationalizing the denominator.
6. (a) Find two irrational number between
2 and
3.
(b) Simplify : 4 3 – 3 12 + 2 75 .
(c) Simplify
5+ 6
5– 6
by rationalizing the denominator.
7. (a) With the help of an example show that difference of two irrationals
need not be an irrational.
(b) Insert three irrational numbers between
2 and
7.
(c) Insert two irrational numbers between 2 and 3.
8. (a) If both a and b are rational numbers, find the values of a and b in the
equality
3–1
3+1
=a+b
3
(b) Rationalize the denominator and simplify
9. (a) If
1
1+ 2 + 3
.
2 = 1.414 find the value of 3 ÷ 6 up to three places
of decimals.
(b) Given that, 3 = 1.7321, find correct to 3 places of decimals the
value of 192 –
1
2
48 – 75 .
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Assignment
10. (a) Simplify :
3
5– 3
+
2
5+ 3
.
(b) Show that
1
3– 8
11. (a) Simplify :
–
1
8– 7
6
2+ 3
+
+
1
7– 6
3 2
6+ 3
–
–
(b) If x = 2 + 3 , find the value of x 2 +
3
1
6– 5
4 3
6+ 2
+
1
5 –2
.
1
.
x2
Assignment
= 5.
Answers
1. (a)
2
3
(b)
63
4
(c) 2.6
2. (a) (ii) and (iii)
3. (a)
(b)
5
12
29
90
(c) 3.1428
(b) (ii) and (iii)
4. (a) (i) 8 and 2
(ii)
2 and 3
(b) irrational number
(c) rational number =
5. (c)
5
, irrational number = 2.303003000...
2
3 2
2
1
1
1
6. (a) 6 4 and 2 4 × 6 8
(b) 8 3
(c)
31 + 10 6
19
7. (a) The two irrational numbers are 5 + 3 and 2 + 3 .
3, 5, 7
(b)
8. (a) a = 2, b = – 1
(c) 2.101001000..., 2.202002000 ...
(b)
2 +2– 6
4
9. (a) 0.707 (b) 1.732
10 (a)
25 + 3
22
11. (a) 0
(b) 14
4
Assignment