when getting the ratio analysis of a companies 4 year income by using the gross profit margin and earnings per share and other probability analysis. What do those numbers represent? For example I have numbers like .654 .541 .410 .504 and I don't know what they mean?

What they represent depends on which ratio they are. Of the two you mentioned, gross profit margin is a percent. (i.e. . 30 means 30% of sales) Earnings per share is money, so .30 means 30 cents. Some of them mean that much per $1 of the thing being compared to.

They all have different meanings.