Explain how knowing that 5÷8=0.625 you write the decimal for 4 5/8

When you trying to write the decimal value of 4 5/8 then you will get 4+ 5/8. If you know how much 5/8 value in decimal form then you don't need to divide 5 with 8. You just need to convert it separately, make it become 4+0.625 = 4.625.

Since you are skipping a stage it definitely helps and making you write the decimal faster.