Assuming $1.23 is in cell A1, in cell B1 use =INT(A1) to return the
whole dollar value.

Then in cell C1 use =MOD(A1,1) to retunr the pennies, 0.23. You can
multiply by 100 if you'd like.

Then add columns B and C individually. Naturally column C may yield a
value of more than 100 pennies.