Rats don't see as well as we do, but they do see things differently. A rat will get a feeling for its environment with his whiskers. Rat's whiskers are the most important thing he has to get a feel for what's around him. A rat will rapidly brush his whiskers along the floor, carpet, cage and even you in order to get a picture of what is around him. Rat's whiskers are more sensitive than humans fingertips in the way they let him know what he is around.
When you're playing with your rat, just watch his whiskers as he walks across the couch, walks along your arm or the floor. They will constantly brush their whiskers along whatever they are next to. They will feel all the tiny indentations, dents, dimples and bumps that we never notice. They know if the surface is smooth, bumpy, or cracked.
Rats have a highly developed sense of smell. As you watch your rat walk around also pay attention to his nose. You will notice his little nose constantly twitching, smelling the air, the carpet, you and any other rats he is around. Your rat may be asleep while you are making dinner but once he gets a whiff of what you're cooking he will most likely be up, jumping around letting you know he smells what's for dinner and he wants some too.
Rats love to stick their noses into small cracks and crevices that hold all sorts of wonderful smells for them. They will try to dig their way through any small opening to find the smell if they like it and they have sharp nails to help with the digging as well as long sharp teeth. Rats love to gnaw on things, so if you let your rat run loose in the living room, expect him to chew on the wooden table legs.
Your rats vision isn't very good, at best what they see more than a few feet away is blurry. That is why a rat will come up to and sniff you, lick you and his ears will twitch when you talk to him.
Because rats are so close to the ground, the things they see are going to be different from what you and I see. If you put your rat on the floor, he isn't going to see just a carpeted floor, he's going to see all the small things on the floor that the vacuum missed the last time you used it, he's going to see a great hiding place behind the couch and a wonderful place to run along the wall.
Rats are very inquisitive, they will seek out fun places to run and climb onto. They will shred your clothes, curtains and any other fabric they find to take back to their nests. They think it would be great bedding material.
Have fun with your rat, but take care where you let him roam as he may get lost, chew up your furniture, wires and walls or just climb somewhere he can't get down without hurting himself.