You could use List::Util::first:

use strict ;
use warnings ;

use List::Util qw(first) ;

my @table = () ;

while (<DATA>) {
  m/^\s*(\S+)\s+(\S+)\s*$/ ;
  push @table, [$1, $2] ;
} ;

@table = reverse sort { $a->[1] <=> $b->[1] ; } @table ;

my @test = (2, 2.69, 2.7, 3.9, 50,  51, 51.1, 200) ;
my @ok   = (0,    1,   1,   5,  7, 170,  171, 171) ;

foreach my $t (@test) {
  my $r = first { $_->[1] <= $t } @table ;

  $r = defined($r) ? $r->[0] : 0 ;

  my $o = shift(@ok) ;
  printf "%7.3f -> %4d  %s\n", $t, $r, $r == $o ? "OK" : "??? expected
+ $o" ;

} ;

__DATA__
    1     2.69
    2     2.97032
    3     3.25064
    4     3.53096
    5     3.81128
    6     4.0916
    7     4.37192
    170   50.98
    171   51.086
[download]

which produces:

  2.000 ->    0  OK
  2.690 ->    1  OK
  2.700 ->    1  OK
  3.900 ->    5  OK
 50.000 ->    7  OK
 51.000 ->  170  OK
 51.100 ->  171  OK
200.000 ->  171  OK
[download]

which appears to be per "specification".

Though you could throw a binary chop at it, if the table is large and it's going to be used a lot:

use strict ;
use warnings ;

my @table = () ;

while (<DATA>) {
  m/^\s*(\S+)\s+(\S+)\s*$/ ;
  push @table, [$1, $2] ;
} ;

@table = sort { $a->[1] <=> $b->[1] ; } @table ;

my @test = (2, 2.69, 2.7, 3.9, 50,  51, 51.1, 200) ;
my @ok   = (0,    1,   1,   5,  7, 170,  171, 171) ;

foreach my $t (@test) {
  my $r = whack(\@table, $t) ;

  $r = defined($r) ? $r->[0] : 0 ;

  my $o = shift(@ok) ;
  printf "%7.3f -> %4d  %s\n", $t, $r, $r == $o ? "OK" : "??? expected
+ $o" ;

} ;

sub whack {
  my ($rt, $v) = @_ ;

  my $t = $rt->[0] ;
  if ($t->[1] > $v) { return undef ; }  # quit if not in table

  my $h = $#$rt ;
  my $l = 0 ;
  my $i ;

  while ($l < $h) {
    $t = $rt->[$i = ($l + $h + 1) >> 1] ;  # new mid index and value

    if ($t->[1] <= $v) {
      last if $t->[1] == $v ;           # quit if exact match
      $l = $i ;                         # entry[$i] <  $v -- move sear
+ch up
    }
    else {
      $h = --$i ;                       # entry[$i] >  $v -- move sear
+ch down past it
    } ;
  } ;

  return $rt->[$i] ;
} ;

__DATA__
    1     2.69
    2     2.97032
    3     3.25064
    4     3.53096
    5     3.81128
    6     4.0916
    7     4.37192
    170   50.98
    171   51.086
[download]