Let's solve this problem step by step. We are given a square paper of length 2.524375cm and a square diagram of length 0.524375cm inscribed on it. We are asked to find the area of the paper not covered by the diagram, correct to 3 significant figures.

First, let's find the area of the square paper. Since the length of each side is 2.524375cm, the area of the square is `(2.524375cm)^2 = 6.37280664cm^2`.

Next, let's find the area of the square diagram. Since the length of each side is 0.524375cm, the area of the square is `(0.524375cm)^2 = 0.27498164cm^2`.

Now, we can subtract the area of the diagram from the area of the paper to find the area not covered by the diagram: `6.37280664cm^2 - 0.27498164cm^2 = 6.09782500cm^2`.

To give the answer correct to 3 significant figures, we need to round this result to the nearest hundredth (since the first two digits after the decimal point are the first two significant figures). The number `6.09782500` rounded to the nearest hundredth is `6.10`.

So, the area of the paper not covered by the diagram is 6.10cm\(^2\)