More conveniently

This can be done more conveniently using Bash's numeric context:

if (( $(echo "$num1 > $num2" |bc -l) )); then
  …
fi

Explanation

Piping through the basic calculator command bc returns either 1 or 0.

The option -l is equivalent to --mathlib; it loads the standard math library.

Enclosing the whole expression between double parenthesis (( )) will translate these values to respectively true or false.

Please, ensure that the bc basic calculator package is installed.

Caveat: Exponential notation should be written as *10^; not E, nor e.

For example:

$ echo "1*10^3==1000" |bc
1

Whereas

$ echo "1E3==1000" |bc
0

Strategies to overcome this bc limitation are discussed here.

Bash handles only integer maths, but you can use the bc command as follows:

$ num1=3.17648E-22
$ num2=1.5
$ echo $num1'>'$num2 | bc -l
0
$ echo $num2'>'$num1 | bc -l
1

Note that the exponent sign must be uppercase.

You can use AWK combined with a Bash if condition:

if awk "BEGIN {exit !($d1 >= $d2)}"; then
    echo "yes"
else
    echo "no"
fi

A pure Bash solution for comparing floats without exponential notation, leading or trailing zeros:

if [ ${FOO%.*} -eq ${BAR%.*} ] && [ ${FOO#*.} \> ${BAR#*.} ] || [ ${FOO%.*} -gt ${BAR%.*} ]; then
  echo "${FOO} > ${BAR}";
else
  echo "${FOO} <= ${BAR}";
fi

The order of logical operators matters. Integer parts are compared as numbers and fractional parts are intentionally compared as strings. Variables are split into integer and fractional parts using this method.

It won't compare floats with integers (without dot).

It's better to use AWK for noninteger mathematics. You can use this Bash utility function:

numCompare() {
   awk -v n1="$1" -v n2="$2" 'BEGIN {printf "%s " (n1<n2?"<":">=") " %s\n", n1, n2}'
}

And call it as:

numCompare 5.65 3.14e-22
5.65 >= 3.14e-22

numCompare 5.65e-23 3.14e-22
5.65e-23 < 3.14e-22

numCompare 3.145678 3.145679
3.145678 < 3.145679

Beware when comparing numbers that are package versions, like checking if grep 2.20 is greater than version 2.6:

$ awk 'BEGIN { print (2.20 >= 2.6) ? "YES" : "NO" }'
NO

$ awk 'BEGIN { print (2.2 >= 2.6) ? "YES" : "NO" }'
NO

$ awk 'BEGIN { print (2.60 == 2.6) ? "YES" : "NO" }'
YES

I solved such problems with such a shell/AWK function:

# Get version of GNU tool
toolversion() {
    local prog="$1" operator="$2" value="$3" version

    version=$($prog --version | awk '{print $NF; exit}')

    awk -vv1="$version" -vv2="$value" 'BEGIN {
        split(v1, a, /\./); split(v2, b, /\./);
        if (a[1] == b[1]) {
            exit (a[2] '$operator' b[2]) ? 0 : 1
        }
        else {
            exit (a[1] '$operator' b[1]) ? 0 : 1
        }
    }'
}

if toolversion grep '>=' 2.6; then
   # Do something awesome
fi

A solution that supports all possible notations, including the scientific notation with both uppercase and lowercase exponents (e.g., 12.00e4):

if (( $(bc -l <<< "${value1/e/E} < ${value2/e/E}") ))
then
    echo "$value1 is smaller than $value2"
fi 

Of course, if you don't need really floating-point arithmetic, just arithmetic on e.g. dollar values where there are always exactly two decimal digits, you might just drop the dot (effectively multiplying by 100) and compare the resulting integers.

if [[ $((10#${num1/.})) < $((10#${num2/.})) ]]; then
    ...

This obviously requires you to be sure that both values have the same number of decimal places.

Please check the below edited code:

#!/bin/bash

export num1=(3.17648*e-22)
export num2=1.5

st=$((`echo "$num1 < $num2"| bc`))
if [ $st -eq 1 ]
  then
    echo -e "$num1 < $num2"
  else
    echo -e "$num1 >= $num2"
fi

This works well.

num1=0.555
num2=2.555


if [ `echo "$num1>$num2"|bc` -eq 1 ]; then
       echo "$num1 is greater then $num2"
else
       echo "$num2 is greater then $num1"
fi

AWK and tools like it (I'm staring at you sed...) should be relegated to the dustbin of old projects, with code that everyone is too afraid to touch since it was written in a read-never language.

Or you're the relatively rare project that needs to prioritize CPU usage optimization over code maintenance optimization... in which case, carry on.

If not, though, instead just use something readable and explicit, such as Python. Your fellow coders and future self will thank you. You can use Python code inline with Bash just like all the others.

num1=3.17648E-22
num2=1.5
if python -c "exit(0 if $num1 < $num2 else 1)"; then
    echo "yes, $num1 < $num2"
else
    echo "no, $num1 >= $num2"
fi

I used the answers from here and put them in a function. You can use it like this:

is_first_floating_number_bigger 1.5 1.2
result="${__FUNCTION_RETURN}"

Once called, echo $result will be 1 in this case, otherwise 0.

The function:

is_first_floating_number_bigger () {
    number1="$1"
    number2="$2"

    [ ${number1%.*} -eq ${number2%.*} ] && [ ${number1#*.} \> ${number2#*.} ] || [ ${number1%.*} -gt ${number2%.*} ];
    result=$?
    if [ "$result" -eq 0 ]; then result=1; else result=0; fi

    __FUNCTION_RETURN="${result}"
}

Or a version with debug output:

is_first_floating_number_bigger () {
    number1="$1"
    number2="$2"

    echo "... is_first_floating_number_bigger: comparing ${number1} with ${number2} (to check if the first one is bigger)"

    [ ${number1%.*} -eq ${number2%.*} ] && [ ${number1#*.} \> ${number2#*.} ] || [ ${number1%.*} -gt ${number2%.*} ];
    result=$?
    if [ "$result" -eq 0 ]; then result=1; else result=0; fi

    echo "... is_first_floating_number_bigger: result is: ${result}"

    if [ "$result" -eq 0 ]; then
        echo "... is_first_floating_number_bigger: ${number1} is not bigger than ${number2}"
    else
        echo "... is_first_floating_number_bigger: ${number1} is bigger than ${number2}"
    fi

    __FUNCTION_RETURN="${result}"
}

Just save the function in a separated .sh file and include it like this:

. /path/to/the/new-file.sh

For simplicity and clarity, just use AWK for the calculations as it's a standard Unix tool and so just as likely to be present as bc and much easier to work with syntactically.

For this question:

$ cat tst.sh
#!/bin/bash

num1=3.17648e-22
num2=1.5

awk -v num1="$num1" -v num2="$num2" '
BEGIN {
    print "num1", (num1 < num2 ? "<" : ">="), "num2"
}
'

$ ./tst.sh
num1 < num2

And for that other question that was closed as a duplicate of this one:

$ cat tst.sh
#!/bin/bash

read -p "Operator: " operator
read -p "First number: " ch1
read -p "Second number: " ch2

awk -v ch1="$ch1" -v ch2="$ch2" -v op="$operator" '
BEGIN {
    if ( ( op == "/" ) && ( ch2 == 0 ) ) {
        print "Nope..."
    }
    else {
        print ch1 '"$operator"' ch2
    }
}
'

$ ./tst.sh
Operator: /
First number: 4.5
Second number: 2
2.25

$ ./tst.sh
Operator: /
First number: 4.5
Second number: 0
Nope...

_{I was posting this as an answer to '4.5: syntax error: invalid arithmetic operator (error token is ".5")' - but the code still seems to work. Why? when it got closed as a duplicate of this question, so here it is as it applies here too.}

This script may help where I'm checking if the installed Grails version is greater than the minimum required.

#!/bin/bash

min=1.4
current=`echo $(grails --version | head -n 2 | awk '{print $NF}' | cut -c 1-3)`

if [ 1 -eq `echo "${current} < ${min}" | bc` ]
then
    echo "Yo, you have an older version of Grails."
else
    echo "Hurray, you have the latest version"
fi

A very simple perl solution:

$ num1=3.2E8
$ num2=2.5E9
$ perl -e "print $num2 > $num1? 'true' : 'false', qq(\n);"
true
$ perl -e "print $num2 < $num1? 'true' : 'false', qq(\n);"
false

This proves that perl really understands the 'E' notation for scientific numerical representation:

$ perl -e "print $num1, qq(\n);"
320000000

If you need a 'if' statment in your shell script, use exit command in perl:

$ if perl -e "exit ($num1 > $num2? 0 : 1);"; then echo true; else echo false; fi
false

Note that in shell script, a command returning 0 is a success, and passes the 'if' condition (so the if-clause is executed). Any other non-zero return values means a failure.

Use KornShell. In Bash you may have to compare the decimal part separately:

#!/bin/ksh
X=0.2
Y=0.2
echo $X
echo $Y

if [[ $X -lt $Y ]]
then
     echo "X is less than Y"
elif [[ $X -gt $Y ]]
then
     echo "X is greater than Y"
elif [[ $X -eq $Y ]]
then
     echo "X is equal to Y"
fi

Use this:

VAL_TO_CHECK="1.00001"
if [ $(awk '{printf($1 >= $2) ? 1 : 0}' <<<" $VAL_TO_CHECK 1 ") -eq 1 ] ; then
    echo "$VAL_TO_CHECK >= 1"
else
    echo "$VAL_TO_CHECK < 1"
fi

Using bashj, a Bash mutant with Java support, you just write (and it is easy to read):

#!/usr/bin/bashj

#!java
static int doubleCompare(double a,double b) {return((a>b) ? 1 : (a<b) ? -1 : 0);}

#!bashj
num1=3.17648e-22
num2=1.5
comp=j.doubleCompare($num1,$num2)
if [ $comp == 0 ] ; then echo "Equal" ; fi
if [ $comp == 1 ] ; then echo "$num1 > $num2" ; fi
if [ $comp == -1 ] ; then echo "$num2 > $num1" ; fi

Of course, the bashj Bash/Java hybridation offers much more...

There's one simple approach which is a bit faster than AWK and does not require bc to be installed. It leverages sort's ability to sort float numbers:

A=1280.4
B=9.325
LOW=$(sort -n <<< "$A"$'\n'"$B" | head -1)
if [[ "$LOW" == "$A" ]]; then
    echo "A <= B"
else
    echo "A >= B"
fi

Of course, it does not work for numbers that are equal.

Just replace the echo with a printf (it understands floats):

st=$(  printf '%50G < %50G\n' "$num1" "$num2" | bc -l  )

A one-liner solution

Suppose you have two variables A and B,

echo "($A > $B) * $B + ($A < $B) * $A" | bc

Here's a gawk+GMP based approach to account for a broader range of potential input :

 echo " 5.65e-23 3.14e-22\n
        5.65 3.14e-2203\n
        3.145678 3.145679\n
        3.25353E+9293 325353e9288\n
        3.14159e+200000000001 3.1415899999999999999999E200000000001\n
        100000 100000.0\n
             4096 4096" \
                         \
 | gawk -v PREC=9999999 -nMbe '
  
   NF+=OFS=sprintf(" %s ",
          (+($!_=sprintf("%24s",$!_)<+$NF) \
     ? "<" \
        : (+$NF<+$!_) \
     ? ">" \
        : (int(+$!_)==(__=int(+$NF)))*\
          (__==+$NF)*index($!_,$NF  )  \
     ? "=" \
         : "\342\211\210")' | ecp 
 
                5.65e-23 < 3.14e-22
                    5.65 > 3.14e-2203
                3.145678 < 3.145679
           3.25353E+9293 ≈ 325353e9288
   3.14159e+200000000001 ≈ 3.1415899999999999999999E200000000001
                  100000 ≈ 100000.0
                    4096 = 4096
 

For more clear-cut cases, it'll give you back a definitive answer of

• less than <,
• greater than >, or
• exactly equal to = (purely integer cases, for now)

When it's relatively ambiguous, it outputs the Unicode character U+2248 ≈ ALMOST EQUAL TO instead of attempting to resolve it at all cost.

Most of the time you won't need PREC of 10-million; something like PREC = 32767 is good enough for most scenarios one encounters on a typical basis.