How to combine exact numbers with measured numbers?

Treat exact numbers as having infinite significant figures and let the measured numbers determine the final precision when combining them in calculations.

When you do a chemistry calculation that mixes exact numbers and measured numbers, think of exact numbers like counting objects or defined values that are perfectly known, for example one dozen equals twelve or one mole equals exactly six point zero two three one four times ten to the twenty three by definition, and measured numbers come from experiments and have limited precision. Use the normal rules for significant figures: for multiplication and division the result should have the same number of significant figures as the measured value with the fewest significant figures, while for addition and subtraction you match the least precise decimal place among the measured values. Exact numbers do not limit precision because they are treated as having infinite significant figures, so they do not reduce the number of significant figures in your answer.

A common mistake is treating exact numbers like measured ones and rounding the result too early, which loses accuracy, so keep intermediate values unrounded and only round the final answer to the correct number of significant figures. Another error is applying addition and subtraction rules to multiplication or division problems, so remember which rule applies: use decimal-place alignment for addition and subtraction and significant-figure counting for multiplication and division. Students also sometimes forget that defined constants such as conversion factors are exact, so do not let those factors determine the precision of your result; let the measured values do that.

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Combining Exact and Measured Numbers

1. Treat exact numbers as infinite precision
2. Use sig figs for multiplication and division
3. Match decimal places for addition and subtraction
4. Keep intermediate values unrounded
5. Round final answer to correct precision

Common Mistakes When Combining Exact & Measured Numbers

1. Treating exact numbers like measured ones
2. Rounding intermediate results too early
3. Misapplying addition/subtraction versus multiplication/division rules

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