Significant Figures Rules and Applications Quiz

Significant Figures

Rules for Determining Significant Figures

Significant figures are the digits in a number that are known with some degree of reliability. The rules for determining significant figures include:

1. All nonzero digits are significant: 1.234 g has 4 significant figures, 1.2 g has 2 significant figures.
2. Zeroes between nonzero digits are significant: 1002 kg has 4 significant figures, 3.07 mL has 3 significant figures.
3. Zeroes to the left of the first nonzero digits are not significant; such zeroes merely indicate the position of the decimal point: 0.0010 C has only 1 significant figure, 0.012 g has 2 significant figures.
4. Zeroes to the right of a decimal point in a number are significant: 0.023 mL has 2 significant figures, 0.200 g has 3 significant figures.
5. When a number ends in zeroes that are not to the right of a decimal point, the zeroes are not necessarily significant: 190 miles may be 2 or 3 significant figures, 50,600 calories may be 3, 4, or 5 significant figures.

Calculations Involving Significant Figures

When performing calculations involving significant figures, it is essential to consider the rules for determining significant figures and round accordingly. The accuracy of a calculated result is limited by the least accurate measurement involved in the calculation. For example, in the calculation 3.000 + 1.5875 = 8.630829, the first division should result in 3 significant figures, the last division should result in 2 significant figures, and the three numbers added together should result in a number that is rounded off to the last common significant digit occurring furthest to the right.

Rounding with Significant Figures

Rounding is a crucial aspect of significant figures. The general rule is that the accuracy of a calculated result is limited by the least accurate measurement involved in the calculation. In rounding, we round off the final digit to the last common digit occurring furthest to the right in all components. For example, if we have two numbers, 100 (assume 3 significant figures) and 23.643 (5 significant figures), their sum is 123.643, which should be rounded to 124 (3 significant figures).

Applications of Significant Figures

Significant figures have various applications in scientific measurements. They are used to report values correctly, indicating the precision of the value. In scientific work, numbers are often the result of averages obtained from multiple experiments. The uncertainty is then given by the standard deviation, rounded off to one digit to obtain the number of significant figures.

Significant Figures in Scientific Measurements

Significant figures are crucial in scientific measurements because they help to convey the precision and uncertainty of the results. They are used to compare a result against a reference interval or a clinical decision point, as well as to monitor treatment by comparing sequential results. In routine chemistry laboratories, results are rounded, and a series of results are 'binned' together. This can hide a significant change in result, so the reporting interval should be such that any result change is greater than the analytical imprecision.