It sure looks like it has a spacebar! Do you mean a Tab key? Terminology is important for communication.

Your separate-keys-for-tabbing system is called decimal tabs. It makes the carriage stop a certain number of spaces before the point where the tab is set so that you can type the number of digits corresponding to the particular tab key you pressed and have all the numerals line up at the right edge of the column. E.g., press the 10 key for a two digit number, the 100 key for a three digit number, the 1M key (1 mil, or 1000) for a four digit number, and so on.

It eliminates the usual single-tab-key practice of tabbing to the set point and then backspacing to allow room for the needed number of digits. Very handy in a business environment. Typewriters with this arrangement are fairly common.

You searched for your serial number on the internet and couldn't find it. Of course not. Why would anybody before you have ever entered this number? This has been out of service since before the internet was invented. Go to the typewriterdatabase.com and look in the Underwood section for the range of serial numbers that includes your number.