MATHEMATE
lon-terminating non-recurring lying between them. Of course, you can find infinite
nany such numbers.
An example of such a number is 0.150150015000150000...
EXERCISE 1.3
1. Write the following in decimal form and say what kind of decimal expansion e
has :
36
100
(iii) 41
(iv) 13
(vi) 400
329
2. You know that = 0.142857. Can you predict what the decimal expansions of
Answers
Answer:
Step-by-step explanation:
We know the terminating and non terminating decimal expansion. Terminating is the one which stops or terminates, but non terminating means it recurs and does not stop.
1. 36 /100 = 0.36. So this is a terminating expansion.
2. 4 1/8 = 4 x 8 = 32 + 1 = 33 / 8
8) 33 (4.125
32
-------------------------------
10
8
----------------------------------------
20
16
-------------------------------
40
40
------------------------------------------
0
So it is a terminating expansion.
3. 3/13
13) 3 (0.23076923
0
-------------------------------
30
26
--------------------------------
40
39
--------------------------------------------------
100
91
-------------------------------------------------
90
78
---------------------------
120
117
--------------------------------
30
26
-------------------------------------
40
39
--------------------------------------
1
So this is non terminating and repeating expansion.
4. 329/400
400) 329 (0.8225
0
- ---------------------------------
3290
3200
-----------------------------------
900
800
---------------------------------------
1000
800
------------------------------------------------
2000
2000
--------------------------------------------------
0
So this is a terminating expansion.
Given You know that 1/7 = 0.142857. Can you predict what the decimal expansions of
7) 1 (0.142857
0
---------
10
7
---------------
30
28
---------------------
20
14
----------------------
60
56
----------------------------
40
35
------------------------------
50
49
-----------------------------
1
We get 3/7 = 0.4285714
2/7 = 0.285714
6/7 = 0.857142
4/7 = 0.571428
5/7 = 0.7142857