The best replacement for integer is double.

The best alternatives to integer are rated as following:
★★★★★  double
★★★★★  long
★★★★★  int
★★★★★  whole number
★★★★  float
★★★★  real number
★★★★  int java
★★★  decimal
★★★  floating point
★★★  long integer
★★  number
★★  simplified fraction
★  number oracle
★  numeric
★  string
★  real numbers
  long vba
  rational number
  int32
  biginteger
  integer
  numeric r
  three is an even integer
  int haskell
  long integer in access
  binary integer
  double vba
  signed integer
  real value

Your alternative for integer is not listed? Suggest!
Speaking about integer, one probably shouldn't forget about another integer.

Other search terms related to integer and their ratings are:
★★★★★ another integer
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integer
double
long