it is true that 81 as recurring decimal equals to 3/55
How to show that 81 as recurring decimal equals to 3/55
From the question, we have the following parameters that can be used in our computation:
1.381818181.....
This can be expressed as
1.3 + 0.081 + 0.00081 + 0.0000081
From the above, we have
First term, a = 0.081
Common ratio, r = 0.01
The sum to infinity on a geometric sequence is
S = a/(1 - r)
So, we have
S = 0.081/(1 - 0.01)
S = 0.081/(0.99)
Evaluate
S = 81/990
Simplify
S = 9/110
This gives
S = 3/55
Hence, 81 as recurring decimal equals to 3/55
Question
Using algebra, show that the 81 in 1.381818181..... equals to 3/55