0.6 : Rules of Significant Figures

The certainty of measurement depends on two factors: the number of digits in the measurement and the precision of the instrument used.

In a measured quantity, all of the digits, including the last uncertain digit, are called significant figures - and can be determined using specific rules.

Any non-zero digits and all captive zeros - which lie between two non-zero digits - are significant. For example, 28 has two significant figures, while 26.25 has four, and 208 has three.

Leading zeros are never significant, as they just locate the decimal point. For example, 0.00208 has three significant figures. Such quantities can be expressed using exponential notations. Thus, 0.00208 can be written as 2.08 × 10⁻³.

Trailing zeros are only significant in decimal formatted numbers. 2200 has two trailing zeros and two significant figures, whereas 2200.0 and 2200.1 both have 5 significant figures.

For quantities without decimal points, the significance of trailing zeros becomes ambiguous. Thus, 2200 can be written as 2.2 × 10³ with two significant figures or 2.20 x 10³with three significant figures.

In any measurement, the precision of the measuring tool is an essential factor. An ordinary ruler, for example, can measure length to the closest millimeter; a caliper, on the other hand, can measure length to the nearest 0.01 mm. As a result, the caliper is a more precise measurement tool because it can measure extremely minute changes in length. The measurements will be more accurate if the measuring tool is more precise.

It should be emphasized that when we represent measured values, the last digit has been calculated in some way by the person making the measurement. For example, a person measuring the length of a stick with a ruler notices that it appears to be between 13.2 cm and 13.3 cm, and so they must estimate the value of the last digit. The rule of significant figures is that the last digit written down in a measurement is the first digit with some uncertainty. Start with the first measured value on the left and count the number of digits through the last digit written on the right to determine the number of significant digits in a value. Significant figures represent the precision of the measuring tool used to measure a value.

The text is adopted from Openstax, University Physics Volume 1, Section: 1.6 Significant Figures.

Tags

Significant Figures Rules Precision Measurement Scientific Notation Rounding Digits Calculations Accuracy Significant Digits

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