A metal rod of length 12.5\text{ cm} is divided into two parts in the ratio 2 : 3. If the … — JAMB UTME

A metal rod of length $12.5\text{ cm}$ is divided into two parts in the ratio $2 : 3$ . If the length of the smaller part is measured as $5.2\text{ cm}$ , what is the percentage error in the measurement of the smaller part?

$4.0\%$ Answer
B
$3.8\%$
C
$1.6\%$
D
$2.7\%$

Answer

The percentage error in the measurement of the smaller part is

4.0\%

The true length of the smaller part of the rod is

\frac{2}{5} \times 12.5 = 5.0\text{ cm}

. Subtracting this from the measured length

5.2\text{ cm}

gives an error of

0.2\text{ cm}

. Dividing the error

0.2\text{ cm}

by the true value

5.0\text{ cm}

and multiplying by

100\%

yields

4.0\%

Step-by-Step Solution

Calculate the actual length of the smaller part using the given ratio.

Total ratio parts =

2 + 3 = 5

. Actual length of smaller part =

\frac{2}{5} \times 12.5\text{ cm} = 5.0\text{ cm}

The total length is shared according to the ratio

2 : 3

, so the smaller piece corresponds to 2 out of 5 equal parts.

Find the absolute error in measurement.

Absolute error =

|5.2\text{ cm} - 5.0\text{ cm}| = 0.2\text{ cm}

Absolute error is the magnitude of the difference between the measured value and the true value.

Compute the percentage error.

Percentage error =

\frac{\text{Absolute Error}}{\text{True Value}} \times 100\% = \frac{0.2}{5.0} \times 100\% = 4.0\%

Percentage error is defined as the absolute error divided by the true value, multiplied by 100%.

Key Concept

Ratio partitioning and Percentage Error calculation

Estimated Time:1m 30s

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