Your Android device's SIM card number is technically called the ICCID, which stands for Integrated Circuit Card Identifier. It usually consists of 19 or 20 characters, and is both printed on your SIM card and stored inside it.
To read the SIM number without ejecting it physically from the device you can use a free application called SIM card. After installing it, open it and you will find the SIM card number on the first line.