Well you could use

print "contains fractional component\n" if $number =~ /\.(?!0*$)/;
[download]

But that'll fail for large numbers.

sub r { $_[0] ? 'fractional' : 'integer' }

for my $n (
   '1.00',
   2**50,
) {
   print(
      "$n:\n",
      "method 1: ", r( $n =~ /\./                      ), "\n",
      "method 2: ", r( $n =~ /\.(?!0*$)/               ), "\n",
      "method 3: ", r( sprintf('%f',$n) =~ /\.(?!0*$)/ ), "\n",
      "method 4: ", r( int($_)!=$_                     ), "\n",
      "\n",
   );
}
[download]

1.00:
method 1: fractional
method 2: integer
method 3: integer
method 4: integer

1.12589990684262e+015:
method 1: fractional
method 2: fractional
method 3: integer
method 4: integer
[download]

Shouldn't one use bignum either ways when going over 32 bit?

Depends. It's a cost-benefit tradeoff. If the use of floats is appropriate, 53 bits of precision is probably way more than enough.

By the way, Perl natively supports (without loss of precision) integer numbers (as in numbers without a fractional component) up to 2**53 (or higher depending on platform and build options), not 2**32-1.

Compare to this demo (which can be written much more compactly but was deliberately written in this tedious manner for utmost clarity):

#!/usr/bin/perl -lw
use strict;

my $number0 = '1.00';    #zwon's version with NON-interpolating quotes
my $number1 = 1.00;
my $number2 = 1.393939393939393939393939393939393939393939393939393939
+3939393939;     # exceeds length for FP precision
my $number3 = 123456789.123e5;
my $number4 = 123e-5;
my $number5 = '123e-5'
;
print "\$number0, $number0, contains a period" if $number0 =~ /\./;
print "\$number0, $number0, is an Integer" if $number0 == int($number0
+);

print "\$number1, $number1, contains a period" if $number1 =~ /\./;
print "\$number1, $number1, is an Integer" if $number1 == int($number1
+);

print "\$number2, $number2, contains a period" if $number2 =~ /\./;
print "\$number2, $number2, is an Integer" if $number2 == int($number2
+);

print "\$number3, $number3, contains a period" if $number3 =~ /\./;
print "\$number3, $number3, is an Integer" if $number3 == int($number3
+);

if ( $number4 =~ /\./ ) {       # alt coding of the previous solely to
+ allow the else
    print "\$number4, $number4, contains a period";
} else {
    print "\tNo period in $number4";
}
print "\$number4, $number4, is an Integer" if $number4 == int($number4
+);

if ( $number5 =~ /\./ ) {
    print "\$number5, $number5, contains a period";
} else {
    print "\tNo period in $number5";
}
print "\$number5, $number5, is an Integer" if $number5 == int($number5
+);

print "\nNext, using ww's regex";
print "\n\$number0: $number0\n\$number1: $number1\n\$number2: $number2
+\n\$number3: $number3\n\$number4: $number4\n";

# CASE 0

$number0 =~ /\d+(\.)\d+/;
if ($1) {
    print "\$number0 contains a decimal point";
}
$number0 =~ s/(\d+)(\.)(\d+)/$1/;
print "Integer value, if desired: $number0";

# CASE 1

$number1 =~ /\d+(\.)\d+/;
if ($1) {
    print "\$number1 contains a decimal point";
}
$number1 =~ s/(\d+)(\.)(\d+)/$1/;
print "Integer value of \$number1, if desired: $number1";

# CASE 2

$number2 =~ /\d+(\.)\d+/;
if ($1) {
    print "\$number2 contains a decimal point";
}
$number2 =~ s/(\d+)(\.)(\d+)/$1/;
print "Integer value of \$number2, if desired: $number2";

# CASE 3

$number3 =~ /\d+(\.)\d+/;
if ($1) {
    print "\$number3 contains a decimal point";
}
$number3 =~ s/(\d+)(\.)(\d+)/$1/;
print "Integer value of \$number3, if desired: $number3";

# CASE 4

$number4 =~ /(\.)/;          # Special case: Scientific notation
if ($1) {
    print "\$number4 contains a decimal point";
}
$number4 =~ s/(\d+)(\.)(\d+)/$1/;
print "Integer  value of \$number4, if desired: $number4";

# CASE 5

$number5 =~ /(\.)/;          # Special case, as above
if ($1) {
    print "\$number5 contains a decimal point";
} else {
    print "NO decimal point in \$number5, $number5";
}
$number5 =~ s/(\d=)(\.)(\d+)/$1/;
print "Integer value of \$number5, if desired: " . int($number5);    #
+ using int(); otherwise prints the string literal
[download]

Output:

$number0, 1.00, contains a period
$number0, 1.00, is an Integer        # --> Note 1
$number1, 1, is an Integer
$number2, 1.39393939393939, contains a period
$number3, 12345678912300, is an Integer
$number4, 0.00123, contains a period
        No period in 123e-5

Next, using ww's regex

$number0: 1.00
$number1: 1
$number2: 1.39393939393939
$number3: 12345678912300
$number4: 0.00123

$number0 contains a decimal point
Integer value, if desired: 1
$number1 contains a decimal point
Integer value of $number1, if desired: 1
$number2 contains a decimal point
Integer value of $number2, if desired: 1
$number3 contains a decimal point
Integer value of $number3, if desired: 12345678912300
$number4 contains a decimal point
Integer  value of $number4, if desired: 0
NO decimal point in $number5, 123e-5
Integer value of $number5, if desired: 0
[download]

Update: revised phrasing of the parenthetical comment about the tedious (kindergarten) code.