Answer:
0.12453300... (the number that goes in the blank)
Explanation:
If we let x represent the value that goes in the blank, then we have ...
x% · 803 = 1
Dividing by 803, we get ...
x% = 1/803 ≈ 0.00124533...(8-digit repeating decimal)
Multiplying the right side by 100% gives ...
x% = 0.124533%
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Additional comment
The rules of equality require we perform the same operation on both sides of the equal sign. Some operations do not change the value of the number, just its form. We know 100% = 1, and multiplying by 1 does not change a number's value. This means we can multiply one side of the equation by 100% without having to do the same thing on the other side.
803 does not have any factors of 2 or 5, so the decimal representation of its reciprocal will repeat. It happens to have an 8-digit repeat.