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awk uses 32-bit floating point numbers, its precision is not infinite. By default it prints to 6 digits, but this can be controlled by the CONVFMT variable. Hopefully this works for your need:
awk...

You've got a pretty good grasp for a newbie, but a couple things of note.

Variables do not expand inside single quotes. Never have, never will. They do inside double quotes, but I don't...

STEP=$1
FILE=$2

sed -n "/Begin CG move = $STEP/,/Begin CG move = $((STEP+1))/p" $FILE > step.$STEP.tmp

x=70
y=$(( $x + 1 ))
sed -n "/Begin CG step $x/,/Begin CG step $y/p" $file

or
awk '/Begin CG step '$x'/ {f=1;next} /Begin CG step '$y'/ {f=0;next} f==1 {print}' file