A Golden Fraction I

\[\frac{100,000,000,000,000,000,000}{99,999,999,989,999,999,999}\]

What is the \(250^{\text{th}}\) digit to the right of the decimal place of the fraction above?

As an explicit example, the \(3^\text{rd}\) digit to the right of the decimal place of 11235.123456789 is 3.


Inspired by Pi Han Goh.
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