a. Rounding to the nearest hundredth means that we only have access to numbers with 2 decimal digits. Our number is enclosed between 45.28 and 45.29. Which one is a better approximation? Well, the one who's closer! To tell how "close" two numbers are, just compute the absolute value of their difference:
[tex]|45.28502
-45.28|=0.00502,\quad |45.28502
-45.29|0.00498[/tex]
So, the distance from 45.29 is less than the distance from 45.28, which makes 45-29 the best approximation.
b. Rounding to the nearest integer means that we can't use decimal digits at all. By the same logic of case (a), we have to choose between 27 and 28: we have
[tex]|27.499-27|=0.499,\quad |
27.499-28|=0.501[/tex]
Which makes 27 the best approximation
c. Rounding to the nearest tenth means that we can only use one decimal digit. Again, the logic is always the same: the number lies between 0.2 and 0.3, and we use the same test to check which is a better approximation:
[tex]|0.224-0.2|=0.024,\quad |0.224-0.3|=0.076[/tex]
Which makes 0.2 the best approximation.
