Exact counts and defined constants do not limit the number of significant figures in a calculation because they are considered to have infinite precision.
Think of significant figures as how sure you are about a measurement, like when you measure length with a ruler. If you count three apples, that count is exact and perfectly certain, so you treat it differently than a measurement that might have some error. Exact numbers come from counting items or from definitions, for example one dozen equals twelve or one mole equals six point zero two two one three seven times ten to the twenty third; those are treated as having unlimited precision. When you multiply or divide by an exact number, you do not reduce the number of significant figures in your result, but when you add or subtract, only the measured values with uncertainty matter for the decimal place rule.
Students often think that every number written in a problem has only a limited number of significant figures, but defined constants and counts are exceptions, so do not let them wrongly reduce your precision. Another common mistake is mixing up when to apply the significant-figure rules for multiplication and division versus addition and subtraction; remember multiplication and division use the number of significant figures while addition and subtraction use decimal places. A quick tip is to track which numbers came from direct measurement versus which were counted or defined, and treat counted or defined values as exact.
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Exact Numbers and Significant Figures
- Significant figures show measurement certainty
- Counts are exact values
- Definitions have unlimited precision
- Multiplying does not reduce sig figs
- Addition/subtraction use decimal places
Common Significant-Figure Mistakes
- Treating all numbers as measured
- Confusing rules for operations
- Forgetting to track exact values
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