Significant Figures

Related Examples and Practice Problems

A worksheet titled 'Significant Figures Worksheet' containing numbers and calculations related to significant figures.
A worksheet titled 'Significant Figures Worksheet' with fill-in-the-blank questions about measurement accuracy, precision, and significant figures with various numerical examples. Includes spaces for name, date, and period.
A physics worksheet titled 'AP WORKSHEET 1a: Significant Figures' with questions about significant figures and calculations, published by Adrian Dingle's Chemistry Pages, revised August 2010.
A page titled 'Chemistry: Significant Digits' explaining rules for significant digits in measurements and calculations, with numbered examples and descriptions.

Topic Summary & Highlights
and Help Videos

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. 

Practice Tips

  • 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.

Topic Overview Podcast

Topic Related Resources

 LABORATORY 
 DEMONSTRATIONS 
 ACTIVITIES 
 VIRTUAL SIMULATIONS 

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.

Video Resources

A document page providing guidelines on how to count significant digits, including rules for non-zero figures, leading zeros, zeros within a number, zeros at the end after a decimal point, and a question prompt about counting significant figures in a specific example.
A black screen showing handwritten numbers, calculations, and arrows in white, red, blue, and black ink, demonstrating mathematical processes or calculations.