What is the connection between the key signature and the number that is used?

What is the connection between the key signature and the number that is used?
If you are referring to music then there is actually no relation. The key signature tells you which key you are going to be playing in. Fir example, 1 sharp on the key signature says you are going to be playing in G major; 2 sharps tell you D major; 3 tell you A major; 1 flat tells you F major; 2 tells you B flat major; and 3 tells you E flat major. (There are more but those are the only ones I know so far). The numbers that are used are called the time signature. The most common of these is 4/4, sometimes represented as a capitol C. The top number in a time signature represent how many beats are in a measure, so in 4/4 there are 4 beats in a measure; in 6/8 there are 6 beats in a measure and so on. The bottom number represents what kind of note gets 1 beat. This part is a little more comfusing. Is the time signature 4/4 there are 4 beats per measure, and a quarter note gets one beat. I don't know why a quarter note is represented by a 4 so don't ask. In 6/8 there are 6 beats in a measure and an eigth note gets one beat.

Here are some other time signatures to make sure you can do it on your own:
3/4


3 beats per measure/ quarter note gets one beat.

4/8


4 beats per measure/ eigth note gets one beat