To understand the percentage difference between two numbers, we first need to understand what percentage means. Percentage is a way of expressing a number as a fraction of 100. For example, 50% means 50 out of 100 or 0.5 as a decimal.

Now, let's look at the problem at hand. We are given two numbers, 45 and 100, and we need to find the percentage difference between them. To do this, we first need to find the absolute difference between the two numbers, which is simply the difference between them without considering whether one is greater than the other. In this case, the absolute difference between 45 and 100 is 100 - 45 = 55.

Next, we need to find the average of the two numbers, which is (45 + 100) / 2 = 72.5. This is the baseline against which we will calculate the percentage difference.

To find the percentage difference, we divide the absolute difference by the average and multiply by 100 to get the percentage. So, the percentage difference between 45 and 100 is:

(55 / 72.5) x 100 = 75.86%

This means that the difference between 45 and 100 is 75.86% of the average of the two numbers. In other words, 45 is 75.86% less than 100.