You can use
#include const int number = 47;
std::stringstream stream;
stream << number;
std::string numberAsString = stream.str();
This way, you are using the power of the STL for you, and are avoiding literally thousands of error possibilities when fiddeling around with char-pointers and string lenghts. The std::string would fit in nicely with the std::vector (or any oher standard container), and as a plus you can get the content as a plain old C-String by calling its c_str()-member. Just to bring regular C++ to the mind, instead of this ugly 30+years old C code floating around here.
Though I speak with the tongues of men and of angels, and have not money, I am become as a sounding brass, or a tinkling cymbal.
George Orwell, "Keep the Aspidistra Flying", Opening words