Matching one of two patterns eases the problem:

use strict;
use warnings;

while (<DATA>) {
    if (/^(10|\d)$/) {
        print "Match for $_";
    } else {
        print "Rejected $_";
    }
}

__DATA__
0
1
9
10
11
20
99
100
[download]

Prints:

Match for 0
Match for 1
Match for 9
Match for 10
Rejected 11
Rejected 20
Rejected 99
Rejected 100
[download]

Update: substituting /^0*(10(\.0+)?|\d(\.\d+)?)$/ for the regex allows leading zeros and decimal fractions. With the test data:

0.1
01
1
1.0
1.01
9.9
10
10.0
10.01
11
20
99
100
[download]

the code prints:

Match for 0.1
Match for 01
Match for 1
Match for 1.0
Match for 1.01
Match for 9.9
Match for 10
Match for 10.0
Rejected 10.01
Rejected 11
Rejected 20
Rejected 99
Rejected 100
[download]