Given:
0.125125125
So, 0.125125125 =
= 0.125 + 0.000125 + 0.000000125 + …
This can be written as
125/103 + 125/106 + 125/109 + …
125/103 [1 + 1/103 + 1/106 + …]
By using the formula,
S∞ = a/(1 – r)
125/103 [1 / (1 – 1/1000)]
125/103 [1 / ((1000 – 1)/1000))]
125/103 [1 / (999/1000)]
125/1000 (1000/999)
125/999
∴ The decimal 0.125125125 can be expressed in rational number as 125/999