0.001 ( bar on 001) when expressed in the form if p/q is
Answers
Question :
0.001 ( bar on 001) express this in p/q form ?
Answer :
Given :
0.001 ( bar on 001)
Required to find :
- p/q form of 0.001 ---- (bar on 001)
Solution :
0.001 (bar on 001)
Period = 001
Periodicity = 3
Since, the Periodicity is 3 .
Multipy the equation 1 with 1000
So,
Multiply with 1000 on both sides ;
Now,
Subtract equation - 1 from equation - 2
Hence ,
We get,
Therefore,
Additional Information :-
What is period ?
Period is the numbers which are repeating .
For example :
Find the period of 5.333---
Here, period = 3
Similarly,
What is periodicity ?
Periodicity is the number of digits which are repeating in that sequence .
For example :
Find the Periodicity of 1.232323----
Here, periodicity = 2
Only a non - terminating repeating / recurring decimal can only be converted into the p/q form .
Let ,
x = 0.001001 .... --- eq (i)
Multiply eq (i) by 1000 , we get
1000x = 1.001001 .... --- eq (ii)
Now , subtract eq (i) from eq (ii) , we get
Hence , 0.001001 .... = 1/999