Use Perl In Bash Script To Compare Floationg Points

Is there a way to compare two floating points numbers in a bash script using perl? I've tried just using a bash if statement and it doesn't seem to support floating point numbers. Can the perl line read vars from bash then output a var to bash?

a=1.1     #from bash
b=1.5     #from bash
if b > a  #perl
then X=1  #perl    X to bash

no need for perl.

#!/bin/ksh

a=1.72
b=1.71

if [ "$(echo "if (${a} > ${b}) 1" | bc)" -eq 1 ] ; then
   echo ">"
else
   echo "<"
fi;

Does it work in just sh? Or is there a way to make just that portion of the script run in ksh if that is needed?

#!/bin/sh

a=1.72
b=1.71

if [ "`echo "if (${a} > ${b}) 1" | bc`" -eq 1 ] ; then
   echo ">"
else
   echo "<"
fi;