You need to use the Symbolic Toolbox, or the MATLAB File Exchange contribution "vpi" (John D'Errico)
The immediate problem you are encountering is that 10^23 requires 77 bits to represent, but IEEE 754 double precision floating point numbers have only 53 bits of precision. Switching to uint64() will not work for you because uint64() would have only 64 bits and you need 77 bits.
The largest power of 10 that MATLAB can store exactly in an IEEE 754 double precision number is 10^15.
The largest power of 10 that can be stored exactly in a uint64() unsigned 64 bit integer is 10^18
