When rounding a number to 2 decimal places, we are essentially keeping only the first two digits after the decimal point and discarding the rest. The third digit after the decimal point is the one that affects the rounding decision.
In this case, the number y is rounded to 9.68, which means that the third digit after the decimal point is either 5 or greater than 5. If it is 5 or greater, we round up the second digit after the decimal point. If it is less than 5, we simply truncate the decimal part.
To find the upper bound of y, we need to add 0.005 to 9.68, which is the smallest possible value for the third digit that would cause rounding up:
9.68 + 0.005 = 9.685
Therefore, the upper bound of y is 9.685.
To find the lower bound of y, we need to subtract 0.005 from 9.68, which is the largest possible value for the third digit that would not cause rounding up:
9.68 - 0.005 = 9.675
Therefore, the lower bound of y is 9.675.
Hence, the upper and lower bounds of y are 9.685 and 9.675, respectively.