JAMB 2023 Mathematics · Question 21

A student is using a graduated cylinder to measure the volume of water and reports a reading of 18 mL. The…

Question

A student is using a graduated cylinder to measure the volume of water and reports a reading of 18 mL. The teacher reports the value as 18.4 mL. What is the student's percent error?

A.2.17%
B.1.73%
C.2.23%
D.1.96%

Answer: A. 2.17%

Explanation written with AI and checked against the answer key

1. Analyze the Question

We are asked to calculate the percent error of a measurement.

Measured Value (Student's reading): 18 mL
Accepted Value (Teacher's reading): 18.4 mL

2. Explain the Concept

Percent error is a measure of how far off a measured value is from the accepted (true) value. The formula is:

\text{Percent Error} = \left| \frac{\text{Measured Value} - \text{Accepted Value}}{\text{Accepted Value}} \right| \times 100\%

Note: The vertical bars indicate the absolute value, meaning the result should always be positive.

3. Show the Solution

Step 1: Find the absolute error.

\text{Absolute Error} = |18 - 18.4|

\text{Absolute Error} = |-0.4| = 0.4 \text{ mL}

Step 2: Divide the absolute error by the accepted value.

\text{Relative Error} = \frac{0.4}{18.4}

To simplify this, multiply both numerator and denominator by 10:

\text{Relative Error} = \frac{4}{184}

\text{Relative Error} = \frac{1}{46} \approx 0.021739...

Step 3: Convert to a percentage.

\text{Percent Error} = 0.021739 \times 100\%

\text{Percent Error} \approx 2.1739\%

Rounding to two decimal places, we get 2.17%.

4. Identify the Answer

Comparing our result to the options provided, the correct choice is A.

5. Exam Tip

When calculating percent error, always remember that the denominator is the Accepted Value (the "true" value provided by the teacher or the standard), not the measured value. A common mistake students make is using their own measurement as the denominator—avoid this to ensure you get the correct answer!

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