30. Emma measured the height of her laptop screen. She reported the height as 8 inches, accurate to the nearest inch. The actual height of the screen must be:
Answer: A
The actual height of the screen must be at least 7.5 inches and less than 8.5 inches.
Emma's measurement of 8 inches, accurate to the nearest inch, indicates that the actual height could range from 7.5 inches to 8.5 inches, as this is the range that would round to 8 inches.
A) at least 7.5 inches and less than 8.5 inches
This option correctly reflects the range of possible actual heights based on the rounding rule. Since Emma measured her laptop screen to be 8 inches, the minimum height that would round up to 8 inches is 7.5 inches, and the maximum height that would still round down to 8 inches is 8.5 inches.
B) at least 7.9 inches and less than 8.1 inches
This option is incorrect because it provides a much narrower range than what is applicable. While the actual height could fall within this range, it does not account for all potential heights that would round to 8 inches, thus failing to encompass the complete range.
C) at least 7.99 inches and less than 8.01 inches
This option is also incorrect because it is excessively restrictive. The actual height could be lower than 7.99 inches and still round to 8 inches. Therefore, this option does not accurately represent the possible range of actual heights.
D) at least 8 inches
This option is incorrect because it ignores all the possible heights below 8 inches that would still round to 8 inches. The height could be as low as 7.5 inches, which makes this option insufficient.
E) exactly 8 inches
This option is incorrect because while 8 inches is one possibility, it does not account for the full range of heights that would round to this measurement. The actual height could also be lower than or higher than 8 inches, specifically within the defined range.
Conclusion
The correct answer, option A, accurately captures the full range of potential actual heights for Emma's laptop screen measurement. All other options either restrict the range too much or fail to recognize the lower limit necessary for rounding to 8 inches. Thus, A is the only option that fulfills the requirement based on the provided measurement.