A student measures the length of a metal rod as 4.0\text{ cm}. If the actual length of the… — JAMB UTME

A student measures the length of a metal rod as $4.0\text{ cm}$ . If the actual length of the rod is $5.0\text{ cm}$ , what is the percentage error in the measurement?

Answer: 20 %

Answer

The percentage error in the measurement is 20%.

The absolute error is the difference between the true length (

5.0\text{ cm}

) and the measured length (

4.0\text{ cm}

), which is

1.0\text{ cm}

. Dividing

1.0\text{ cm}

by the true length

5.0\text{ cm}

gives a fractional error of

0.20

. Expressed as a percentage,

0.20 \times 100\% = 20\%

Step-by-Step Solution

Find the error (difference between measured value and actual value)

Error =

|5.0\text{ cm} - 4.0\text{ cm}| = 1.0\text{ cm}

Absolute error is defined as the magnitude of the difference between the actual value and the measured value.

Calculate the percentage error

Percentage error =

\frac{1.0\text{ cm}}{5.0\text{ cm}} \times 100\% = 20\%

Percentage error is the ratio of absolute error to the actual value, expressed as a percentage.

Key Concept

Percentage Error Calculation

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