How do you determine the accuracy of a measurement?

You determine the accuracy of a measurement by comparing it to a known standard or true value.

To delve deeper, accuracy refers to how close a measured value is to the actual or true value. For example, if you are measuring the length of a table and the true length is 2 metres, an accurate measurement would be very close to 2 metres. To assess accuracy, you often need a reference or standard value to compare your measurement against. This reference could be a value provided by a highly precise instrument or a value agreed upon by experts.

One way to determine accuracy is by calculating the percentage error. The formula for percentage error is:

\[ \text{Percentage Error} = \left( \frac{|\text{Measured Value} - \text{True Value}|}{\text{True Value}} \right) \times 100 \]

For instance, if you measure the length of the table as 1.95 metres, the percentage error would be:

\[ \text{Percentage Error} = \left( \frac{|1.95 - 2.00|}{2.00} \right) \times 100 = 2.5\% \]

A smaller percentage error indicates a more accurate measurement.

Another method is to use repeated measurements. By taking multiple measurements and calculating the average, you can reduce random errors and get a value closer to the true value. If your measurements are consistently close to the true value, they are considered accurate.

In summary, accuracy is about how close your measurement is to the true value, and you can determine it by comparing your measurement to a known standard, calculating percentage error, and using repeated measurements.