H2 Physics 1 - Quantities and Measurement: Percentage Uncertainty

Step 1 - Read the problem

A student measures the diameter of a wire using a micrometer screw gauge.

Step 1 - Read the problem

She records five readings: 0.52, 0.54, 0.51, 0.53, and 0.52 mm.

Step 1 - Read the problem

Find the mean diameter and the percentage uncertainty.

Step 2 - Calculate the mean

Add all five readings and divide by five.

Step 2 - Calculate the mean

The sum is 2.62 mm.

Step 2 - Calculate the mean

Dividing by five gives a mean of 0.524 mm.

Step 3 - Find the uncertainty from the spread

The uncertainty in the mean is half the range.

Step 3 - Find the uncertainty from the spread

Max is 0.54, min is 0.51, so the range is 0.03 mm.

Step 3 - Find the uncertainty from the spread

Half the range gives an uncertainty of 0.015 mm.

Step 4 - Calculate the percentage uncertainty

Percentage uncertainty equals delta d over d bar, times one hundred percent.

Step 4 - Calculate the percentage uncertainty

Substituting: 0.015 divided by 0.524, times 100.

Step 4 - Calculate the percentage uncertainty

This gives approximately 2.9 percent.

Step 5 - State the final answer with correct significant figures

The micrometer reads to the hundredths place in mm, so round the mean to 0.52 mm.

Step 5 - State the final answer with correct significant figures

The final result: d = 0.52 plus or minus 0.02 mm, with a percentage uncertainty of about 3%.

Step 5 - State the final answer with correct significant figures

Key rule: round the uncertainty to one significant figure, then match the mean to the same decimal place.