ACT Math · Ratios, rates, and percents

The actual length of an object is 50 centimeters, but a student measures it as 47 centimeters. What is the percent error of the measurement?

The actual length of an object is 50 centimeters, but a student measures it as 47 centimeters. What is the percent error of the measurement?

Answer and explanation

Answer: G: 6%

Percent error is the size of the error divided by the actual value, times 100%100\%: ∣50−47∣50⋅100%=350⋅100%=6%\frac{|50-47|}{50}\cdot100\%=\frac{3}{50}\cdot100\%=6\%, choice G. Choice H (6.4%6.4\%) divides the error by the measured value, 347\frac{3}{47}, but percent error always compares to the true value. Choice F (3%3\%) is the absolute error of 33 centimeters, written as a percent without dividing by the actual value. Choice J (94%94\%) is 4750\frac{47}{50}, the measurement as a percent of the actual length, not the error.

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