This state transition diagram only shows forward transitions. Failure transitions will move to Integer, Sign, DecPt, or S0, if the input character is [0-9], [+ -], [.], or other, respectively.
Based on this State Transition Diagram we can develop the following Right Regular Grammar. Each state is represented by a nonterminal symbol of the grammar. There are four states which are possible terminal states, namely - Integer, Decimal, Mantissa, and Float. The productions that correspond to a transition to one of these four states must include the production which reduces to the terminal symbol that defines the transition.
Sigma -> [0-9]A -> [0-9] -> [+-]B -> [.]C A -> [0-9]A -> [0-9] -> [.]D -> [.] -> [eEdD]E B -> [0-9]A -> [0-9] -> [.]C C -> [0-9]F -> [0-9] D -> [0-9]F -> [0-9] -> [eEdD]E E -> [+-]G -> [0-9]H -> [0-9] F -> [0-9]F -> [0-9] -> [eEdD]E G -> [0-9]H -> [0-9] H -> [0-9]H -> [0-9]