Significant Figures

Core Concept

Significant figures, also known as significant digits or sig figs, provide a way to convey the reliability and limitations of measurements and calculations. They indicate the precision of a measurement and convey the level of certainty or uncertainty associated with it.

Significant figures reflect the precision of a measurement or calculation and must align with the least precise value used.
Ignoring Rules for Zeros: Misidentifying leading, captive, or trailing zeros.
Forgetting the Input Precision: Failing to adjust significant figures in calculations to match the least precise measurement.
Mixing Up Decimal Places and Significant Figures: Decimal places matter only in addition/subtraction; significant figures are the focus in multiplication/division.

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Assorted Multiple Choice

A student measures the mass of a sample as $0.05020\text{ g}$. How many significant figures are in this measurement?

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Significant Figures

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Counting Significant Figures

  
                Rule
                Examples
            
                If there is a decimal point present, start at the LEFT and count, beginning with the first non-zero digit.
                
                    340. → 3 significant figures

                    30400. → 5 significant figures

                    0.34955 → 5 significant figures

                    0.00500 → 3 significant figures
                
                If there is NOT a decimal point present, start at the RIGHT and count, beginning with the first non-zero digit.
                
                    340 → 2 significant figures

                    30400 → 3 significant figures

                    34955 → 5 significant figures
                
                Counting numbers, conversions, and accepted values have unlimited (infinite) significant figures.
                Examples: 12 apples, 1 inch = 2.54 cm (exact conversion)

The rules above is

Rules for Significant Figures in Calculations

Addition and Subtraction

For addition and subtraction, the answer is limited by the number of decimal places of the least precise measurement. The result should be rounded so it has the same number of decimal places as the number with the fewest decimal places.

Example: 12.34+0.6=12.94. The number 12.34 has two decimal places, while 0.6 has only one. Therefore, the answer must be rounded to one decimal place, giving 12.9.

Multiplication and Division

For multiplication and division, the answer is limited by the number of significant figures of the least precise measurement. The result should be rounded to have the same number of significant figures as the number with the fewest significant figures.

Example: 4.56×1.4=6.384. The number 4.56 has three significant figures, while 1.4 has two. The result must be rounded to two significant figures, giving 6.4.

Logarithms

For a logarithm, the number of decimal places in the result should equal the number of significant figures in the original number.

Example: log(4.56)=0.659. The input value, 4.56, has three significant figures. Therefore, the result should be rounded to three decimal places, giving 0.659.

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