The edge of the ball falls the marks for 13 feet 10 1/8 inches and 13 feet 10 1/4 inches, so he rounds to the eighth of an inch closest to where his ball landed, which is 13 feet 10 1/8 inches. At her school, Lacey fires her cataplult and measures the distance. Her distance falls between the same two marks, but she reports her distance as 13 feet 10 3/16 inches and claims she’s won.
a. What measurement error did Lacey make?
b. The judges declare a tie, but is it possible that Randal would have won if they used a measuring tape with higher precision? Explain why or why not.
a. The measurement error Lacey made is rounding to the sixteenth of an inch instead of the eighth of an inch. She reported her distance as 13 feet 10 3/16 inches, which falls between the marks 13 feet 10 1/8 inches and 13 feet 10 1/4 inches. However, since Randal rounded to the eighth of an inch (13 feet 10 1/8 inches), Lacey's measurement is not in the closest eighth of an inch to where the ball landed.
b. It is not possible for Randal to win even with a measuring tape of higher precision. This is because both Randal and Lacey's distances fall between the same two marks (13 feet 10 1/8 inches and 13 feet 10 1/4 inches). Even if the measuring tape had higher precision and allowed for more decimal places, the difference between Randal's measurement (13 feet 10 1/8 inches) and Lacey's measurement (13 feet 10 3/16 inches) would still remain the same. The only way Randal could have won is if his ball landed closer to the 13 feet 10 1/4 inch mark, but since it landed closer to the 13 feet 10 1/8 inch mark, Lacey's claim for victory is still invalid.