Question 28

The actual height of the screen must be at least 7.5 inches and less than 8.5 inches.

When Emma reports the height of her laptop screen as 8 inches, accurate to the nearest inch, it indicates that the actual height could range from 7.5 inches to just below 8.5 inches.

A) at least 7.5 inches and less than 8.5 inches.

This option is correct because when a measurement is reported as accurate to the nearest inch, the range includes all values that round to 8 inches. Therefore, the actual height must be no less than 7.5 inches and must not reach 8.5 inches.

B) at least 7.9 inches and less than 8.1 inches.

This option is incorrect as it suggests a much narrower range than what is applicable. The actual height could be less than 7.9 inches or more than 8.1 inches and still round to 8 inches when measured accurately to the nearest inch.

C) at least 7.99 inches and less than 8.01 inches.

This option is also incorrect because it restricts the height to an unreasonably narrow margin. While it does include values that round to 8 inches, it ignores the full range up to 8.5 inches, which is essential to consider.

D) at least 8 inches.

This option is incorrect since it excludes all values below 8 inches that would still round to 8 inches, specifically those from 7.5 inches up to but not including 8.5 inches.

E) exactly 8 inches.

This option is incorrect because it suggests a single height rather than a range. The actual height could vary while still being reported as 8 inches, encompassing all values from 7.5 inches to just under 8.5 inches.

Conclusion

The correct answer is A, as it accurately reflects the entire range of possible actual heights based on the reported measurement. All other options fail by either restricting the range too narrowly or not encompassing the entire spectrum of heights that can round to 8 inches.