Diego measured the length of a pen to be 22 cm. The actual length of the pen is 23 cm: Which of these is closest to the percent error for Diego’s measurement? 4.3% 4.5% 95.7% 104.5%
The Correct Answer and Explanation is:
To find the percent error in Diego’s measurement, we use the formula for percent error:Percent Error=(∣Measured Value−Actual Value∣Actual Value)×100\text{Percent Error} = \left( \frac{|\text{Measured Value} – \text{Actual Value}|}{\text{Actual Value}} \right) \times 100Percent Error=(Actual Value∣Measured Value−Actual Value∣)×100
Measured value = 22 cm
Actual value = 23 cmPercent Error=(∣22−23∣23)×100=(123)×100≈4.35%\text{Percent Error} = \left( \frac{|22 – 23|}{23} \right) \times 100 = \left( \frac{1}{23} \right) \times 100 \approx 4.35\%Percent Error=(23∣22−23∣)×100=(231)×100≈4.35%
The closest answer choice is 4.3%.
Explanation
Percent error is a way to describe how accurate a measured value is when compared to the actual or true value. It tells us how far off a measurement is, expressed as a percentage of the actual value. This is useful in science, engineering, and everyday situations where measurements are involved.
In this problem, Diego measured the length of a pen to be 22 centimeters, but the actual length was 23 centimeters. To determine how accurate Diego’s measurement was, we use the percent error formula.
The formula requires us to subtract the measured value from the actual value, take the absolute value of the difference, divide that by the actual value, and then multiply by 100 to convert it to a percentage.
Here, the difference between the measured and actual lengths is 1 centimeter. Taking the absolute value ensures we ignore whether the error is positive or negative. Then, dividing by the actual length, 23 centimeters, we get the fraction of the error relative to the actual size. Multiplying by 100 converts this fraction into a percent.
The resulting value is approximately 4.35 percent. Since the question is asking for the closest answer, and the available options are 4.3%, 4.5%, 95.7%, and 104.5%, the correct answer is 4.3%.
The other options are clearly incorrect because 95.7% and 104.5% would indicate that the error was nearly equal to or more than the actual value, which is not the case here. Diego’s measurement was only slightly off by 1 centimeter.
