Maths Quest Maths C Year 11 for Queensland
Chapter 1 Number Systems: The Real Number System WorkSHEET 1.1
1
WorkSHEET 1.1 Number systems: The Real Number System
Name: _________________________
Irrational numbers are 11 , 4  , and e.
1
Which of these are irrational numbers?
.
1
19, 11 , 4  ,
, 5. 6 , e = 2.71828…
9
2
Express the recurring decimal 0.6 3 as a
fraction in its simplest form.
3
Classify each of these elements of the set
15
15

{ 3,
,  4.7, 
, 19 , } into the
2
3
6
smallest subset to which they belong using
Q (rational), Q (irrational), Z(integers),
Z+(positive integers), and Z–(negative integers).
3  Z
15
= 7.5  Q
2
4.7  Q
15

= 5  Z
3
19 = 4.358 898 944 (non-terminating and
non-recurring)  Q

= 0.523 598 7756 (non-terminating and
6
non recurring)  Q
3
4
Classify each of the elements of the set
15
14

{6,
, 4.9,  , 29 , } into the smallest
2
7
3
subset to which they belong using Q (rational),
Q (irrational), Z(integers), Z+(positive integers)
and Z–(negative integers).
6  Z+
15
= 7.5  Q
2
4.9  Q
14
 = 2  Z
7
29 = 5.385 164 807  Q

= 1.047 197 551  Q
3
3
Let x = 0.6363 63…
100x = 63.636 363…
100x  x = 63
99x = 63
99 x 63

99 99
63
x=
99
7
x=
11
1
2
Maths Quest Maths C Year 11 for Queensland
Chapter 1 Number Systems: The Real Number System WorkSHEET 1.1
= 0.777 777…
= 7.777 777…
=7
=7
7
=
9
7
x =
9
2
5
Express the recurring decimal 0. 7 as a fraction
in its simplest form.
Let x
10x
10x  x
9x
9x
9
6
Express the recurring decimal 0.4 3 as a
fraction in its simplest form.
Let x
100x
100x  x
99x
99x
99
7
Which of these set of fractions can be
expressed as a recurring decimal?
1 3
2
, , 0.262626…,
11 8
5
1
= 0.090 909…
11
3
= 0.375
8
2
= 0.4
5
1
Thus
and 0.262 626… can be expressed as
11
a recurring decimal.
1
8
Select the integers from:
14

7,  ,  4.6, 9 , , 10
6
3
The integers are 7,
1
9
Which of the set of numbers
16 3
36 , 8 ,
, 8 , 22 are surds?
25
36 = 6
8 = 2.828 427 125… non-recurring and
non-terminating
16 4
= = 0.8
25 5
3
8 =2
22 = 4.690 415 76… non-recurring and
non-terminating
Thus 8 and 22 are surds.
= 0.434 343…
= 43.434 343…
= 43
= 43
43
=
99
43
x =
99
9 and 10.
2
2
2