Pigols and Egols

Algebra Level pending

A pigol (PIE gol) is defined as being equal to \(\left\lfloor { 10 }^{ 99 }\pi \right\rfloor\). An egol (EE gol) is defined as being the somewhat smaller \(\left\lfloor { 10 }^{ 99 }e \right\rfloor\).

When the product of a pigol and an egol are written in the form \({ 10 }^{ x }\), what are the first three digits after the decimal point of \(x\)?

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