Natural Numbers, Integers, Rational Numbers Worksheet With Answers - Mathematics Secondary Course Page 21
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36MODULE -
1
Number Systems
Algebra
Let us consider another example.
Example 14:
Write the decimal representation of each of the following:
7
2
5
( )
( )
( )
a
b
c
Notes
3
7
11
. 2
33
Solution:
(a)
Here the remainder 1 repeats.
3
. 7
00
6
∴ The decimal is not a terminating decimal
1.0
7
9
=
. 2
333
...
or
2
3 .
1.0
3
9
1.00
. 0
28571428
(b)
7
. 2
000
Here when the remainder is 3, the digit after
14
that start repeating
60
56
2
=
. 0
285714
40
7
35
Note:
A bar over a digit or a group of digits
50
implies that digit or that group of digits starts
49
repeating itself indefinitely.
10
7
30
28
20
14
60
56
4
. 0
454
(c)
11
5.00
Here again when the remainder is 5, the digits
44
after 5 start repeating
60
55
5
∴
=
. 0
45
50
11
44
50...
Mathematics Secondary Course
23
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