Let x = 0.151515.... (1)
Notice the number of integers that are repeating. Here 1 and 5 are repeating.
So, multiply both sides of the above expression by 100. (If only one integer is repeating, you need to multiply by 10, if 3 integers repeating, you need to multiply by 1000 and so on.)
So, (1) becomes,
100x = 15.151515.... (2)
(2) - (1) gives,
99x = (15.151515.....) - (0.151515....)
= 15
[tex]x=\frac{15}{99}[/tex]
Hey there!!
The decimal given - 0.15151515
Let's take this given decimal as ' x '
As the periodicity is 2 we multiply x and the number by 100.
What is periodicity?
Ans - Periodicity is the number of digits repeating.
In the given decimal, the number repeating is 15, and the number of digits is equal to 2 and hence periodicity is 2.
If the periodicity is 1, then we multiply by 10 and if it is 3 , then we multiply with 1000 and continues.
We have got :
x = 0.1515151515
100 ( x ) = 100 ( 0.151515151515 )
... 100x = 15.151515
The two equations we got :
100x = 15.1515 ------- ( 1 )
x = 0.1515 --------- ( 2 )
Now, let's subtract the second equation from the first.
We get ,
... 99x = 15
Divide 99 on both sides
... x = 15 / 99
At the start we knew x = 0.151515
Now plug in the value
0.151515 = 15 / 99
Hence, the fractional or the rational form of 0.151515 is 15/99
Simplified answer - 5 / 33
Hope my answer helps!!
