You have 
. Rounding this number to the nearest thousandth means to write it as the three-decimal-digits number which is nearest to this one.
The two numbers with three decimal digits are 1.763 and 1.764. Since the fourth decimal digit is 4, your number is closer to 1.763 than 1.764, so this is its approximation.
The two numbers with three decimal digits are 1.763 and 1.764. Since the fourth decimal digit is 4, your number is closer to 1.763 than 1.764, so this is its approximation.