“Invalid Arithmetic Operator” when doing floating-point math in bash

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bash does not support floating-point arithmetic. You need to use an external utility like bc.

# Like everything else in shell, these are strings, not
# floating-point values
d1=0.003
d2=0.0008

# bc parses its input to perform math
d1d2=$(echo "$d1 + $d2" | bc)

# These, too, are strings (not integers)
mean1=7
mean2=5

# $((...)) is a built-in construct that can parse
# its contents as integers; valid identifiers
# are recursively resolved as variables.
meandiff=$((mean1 - mean2))

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