Question

Question13. Convert the following decimal number in the form𝑝
𝑞
.
a. 0.123̅
b. 0.003̅52̅̅̅

Answer 1

a)0.123333..... = x.......(a)
Periodicity=10
multiply 10 on both sides
10x=1.2333... ........(b)
Subtract statement 'a' from statement 'b'
10x=1.2333...
x=0.1233...
.............................
9x=1.1100
----------------------
x=1.11/9
x=111/900

b)0.00353535... = x........(a)
Periodicity=100
multiply 100 on both sides
100x=0.3535... .......(b)
Subtract statement 'a' from statement 'b'
100x=0.3535...
x=0.00353....
.............................
99x=0.3500
----------------------
x=0.35/99
x=35/9900