Explain the role of significant figures in limits of accuracy.

Significant figures indicate the precision of a measurement and help determine the limits of accuracy in calculations.

When you measure something, the number of significant figures tells you how precise that measurement is. For example, if you measure a length as 12.3 cm, it has three significant figures, meaning the measurement is precise to the nearest tenth of a centimetre. This precision is crucial because it affects how accurate your calculations will be when you use this measurement.

In calculations, the number of significant figures in your final answer should reflect the precision of the least precise measurement you used. For instance, if you multiply 12.3 cm (three significant figures) by 4.56 cm (three significant figures), your answer should also be rounded to three significant figures. This ensures that your result is not misleadingly precise.

Significant figures also help in understanding the limits of accuracy. If a measurement is given as 12.3 cm, the true value could be anywhere between 12.25 cm and 12.35 cm. This range is the limit of accuracy, and it’s important to consider this when making further calculations or measurements. Ignoring significant figures can lead to errors and overconfidence in the precision of your results.

In summary, significant figures are a way to communicate the precision of measurements and ensure that calculations reflect this precision, maintaining the integrity and accuracy of your mathematical work.