1. Jada measured the height of a plant in a science experiment and finds that, to the 1/4 nearest of an inch, it is 3/4 inches.

a. What is the largest the actual height the plant could be?

b. What is the smallest the actual height the plant could be?

c. How large could the percent error in Jada's measurement be?

Question

Mathematics

Kaia

23 July, 04:34

1. Jada measured the height of a plant in a science experiment and finds that, to the 1/4 nearest of an inch, it is 3/4 inches.

a. What is the largest the actual height the plant could be?

b. What is the smallest the actual height the plant could be?

c. How large could the percent error in Jada's measurement be?

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Answers (1)

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Rachel · Answer 1

Given that the height (h) of the plant to the nearest 1/4 of an inch is 3/4 inches = 0.75 inches.

It is obvious that the height will lie within the range

2.5/4
which corresponds to the range

5/8
Thus,

a. The largest actual height could be 0.875 inches, while

b. The smallest actual height could be 0.625 inches

c. The percentage error is given by the formula:

[ (approx.-exact) / exact]*100%

If we take the lowest value, for instance, as the exact, i. e. 0.625 inches,

then % error = [ (0.75-0.625) / 0.75]*100% = 16.7%

Obviously, the same value is expected if we take the upper limit of 0.875, i. e. % error = [ (0.75-0.875) / 0.75]*100% = - 16.7%, only that the absolute value will be taken.