A number 𝑦, when rounded to 2 significant figures, is equal to 4.6Find the upper and lower bound of 𝑦.

To find the upper and lower bounds of a number when it is rounded to a certain number of significant figures, you need to consider what the number could have been before rounding.

1. Lower Bound: The number y is rounded to 4.6, so the original number could be anything up to, but not including, half way to the next number when rounded to the same significant figures. The next number after 4.6, when rounded to 2 significant figures, is 4.7. Half way between 4.6 and 4.7 is 4.65. So, the lower bound of y is 4.65.

2. Upper Bound: Similarly, the original number could be anything more than, but not including, half way to the previous number when rounded to the same significant figures. The previous number before 4.6, when rounded to 2 significant figures, is 4.5. Half way between 4.5 and 4.6 is 4.55. So, the upper bound of y is 4.55.

Therefore, the lower bound of y is 4.55 and the upper bound is 4.65.