To find out how many times higher the number of library visits one week before the examination day is compared to the average number of visits in a week, we will divide the number of visits recorded during the examination week by the average number of visits.
The number of visits one week before the examination is approximately \(2 \times 10^3\).
The average number of visits is approximately \(5 \times 10^2\).
Now, let's calculate the ratio:
\[ \text{Ratio} = \frac{2 \times 10^3}{5 \times 10^2} \]
To simplify this, we can divide the coefficients (the numbers in front) and subtract the exponents on the powers of 10:
\[ \text{Ratio} = \frac{2}{5} \times \frac{10^3}{10^2} = \frac{2}{5} \times 10^{3-2} = \frac{2}{5} \times 10^1 = \frac{2}{5} \times 10 = \frac{20}{5} = 4 \]
Thus, the number of library visits before examination day is 4 times higher than the number of library visits in an average week.