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
at least 7.5 inches and less than 8.5 inches.
Emma reported the height of her laptop screen as 8 inches, accurate to the nearest inch. This means the actual height can range from 7.5 inches to just below 8.5 inches, encompassing all values that would round to 8 inches.
This choice accurately reflects the rounding principle. Since Emma's measurement is rounded to the nearest inch, the actual height must be within the range of 7.5 to just under 8.5 inches to ensure it rounds to 8 inches.
This choice is too restrictive. While it falls within the range of acceptable heights that would round to 8 inches, it excludes valid measurements such as 7.6 inches to 7.9 inches and 8.1 inches to 8.4 inches, which would also round to 8 inches.
This option is overly precise. While it includes a tiny range that rounds to 8 inches, it excludes a significant number of valid heights, such as 7.5 inches to 7.98 inches or 8.02 inches to 8.49 inches, that would also round to 8 inches.
This choice fails to account for all lower values that could round to 8 inches. It implies that the height could not be less than 8 inches, which contradicts the rounding rule that allows for heights as low as 7.5 inches.
While this choice is technically correct for one specific measurement, it does not account for the range of values that could round to 8 inches. The height could be any value within the specified range, not limited to just 8 inches.
Accurate reporting of measurements requires understanding rounding principles. Emma's measurement of 8 inches allows for a range from 7.5 to just under 8.5 inches, making option A the only correct choice. The other options either restrict the range too much or misinterpret the rounding criteria, leading to incorrect conclusions about the actual height of the laptop screen.
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