Final answer:
The number 0.00419 is written as the fraction 419/1000, which is in its simplest form as 419 and 1000 do not have any common factors other than 1.
Step-by-step explanation:
To write the number 0.00419 as a fraction in its simplest form, we need to identify how many places the decimal point has been moved.
In this number, the decimal point has moved 3 places to the right to get from the standard form to its decimal place value.
So, we can express 0.00419 as 419 over 10 to the power of 3, which is 1000, giving us the fraction 419/1000.
This fraction cannot be simplified any further since 419 and 1000 do not have any common factors other than 1.
Therefore, 419/1000 is the fraction in its simplest form.