Question

The true length of a wire is 3.678 cm. When the length of this wire is measured using instrument A, the length of the wire is 3.5 cm. When the length of the wire is measured using instrument B, it is found to have length 3.38 cm. Then the

• A. measurement with A is more acurate while measurement with B is more precise.
• B. measurement with B is more accurate and precise.
• C. measurement with A is more precise while measurement with B is more accurate.
• D. measurement with A is more accurate and precise.

Answer 1

The Correct Option is A

Given: 

• True length of the wire: 3.678 cm
• Measured length using instrument A: 3.5 cm
• Measured length using instrument B: 3.38 cm

Step 1: Understanding Accuracy and Precision

• Accuracy: How close the measurement is to the actual value.
• Precision: How close repeated measurements are to each other.

Step 2: Comparing Measurements

Accuracy is determined by comparing the measured value to 3.678 cm:

• Error in A: \( |3.5 - 3.678| = 0.178 \)
• Error in B: \( |3.38 - 3.678| = 0.298 \)

Since 3.5 cm is closer to 3.678 cm than 3.38 cm, instrument A is more accurate.

Precision is determined by the number of significant figures:

• Instrument A measures up to 2 decimal places.
• Instrument B measures up to 3 decimal places, implying higher precision.

Step 3: Conclusion

The measurement with A is more accurate, while measurement with B is more precise.

Answer: The correct option is A.

Answer 2

To determine which instrument provides a more accurate and precise measurement, we need to understand the concepts of accuracy and precision:

Accuracy refers to how close the measured value is to the true value.
Precision refers to how consistent the measurements are when repeated under the same conditions.

Given:
- The true length of the wire is \(3.678\) cm.
- Measurement with instrument A gives \(3.5\) cm.
- Measurement with instrument B gives \(3.38\) cm.

Accuracy:
- The measurement with instrument A is \(3.5\) cm, which is closer to the true value of \(3.678\) cm.
- The measurement with instrument B is \(3.38\) cm, which is farther from the true value.

Therefore, instrument A is more accurate.

Precision:
- The precision of an instrument is determined by how many significant digits the instrument can measure. Instrument B has reported a value to two decimal places (\(3.38\)), while instrument A reports only one decimal place (\(3.5\)).

Thus, instrument B is more precise.

Since the measurement with instrument A is more accurate and instrument B is more precise, the correct answer is:

\[{\text{(A) measurement with A is more accurate while measurement with B is more precise.}}\]