If the circumference of a circle is measured as 31.4 cm with an error of 0.2 cm,

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Question: If the circumference of a circle is measured as 31.4 cm with an error of 0.2 cm, what is the percentage error?

Options:

Correct Answer: 0.64%

Solution:

Percentage error = (Absolute error / Measured value) * 100 = (0.2 / 31.4) * 100 ≈ 0.64%.

If the circumference of a circle is measured as 31.4 cm with an error of 0.2 cm, what is the percentage error?

If the circumference of a circle is measured as 31.4 cm with an error of 0.2 cm, what is the percentage error?

Step 1: Identify the measured value of the circumference, which is 31.4 cm.
Step 2: Identify the absolute error, which is 0.2 cm.
Step 3: Use the formula for percentage error: Percentage error = (Absolute error / Measured value) * 100.
Step 4: Substitute the values into the formula: Percentage error = (0.2 / 31.4) * 100.
Step 5: Calculate the division: 0.2 divided by 31.4 equals approximately 0.006366.
Step 6: Multiply the result by 100 to convert it to a percentage: 0.006366 * 100 equals approximately 0.6366.
Step 7: Round the result to two decimal places: 0.6366 is approximately 0.64%.
Step 8: Conclude that the percentage error is approximately 0.64%.

Percentage Error – The percentage error is a measure of how inaccurate a measurement is, expressed as a percentage of the measured value.
Absolute Error – The absolute error is the difference between the measured value and the true value, indicating the magnitude of the error.
Circumference of a Circle – The circumference of a circle is calculated using the formula C = 2πr, where r is the radius.