Does multiplying by an exact count change sig figs?

No, multiplying a measured quantity by an exact count does not change the number of significant figures; the measured value’s significant figures still determine the result.

Think of a measured value like a number with only so many reliable digits, and an exact count like a perfect, known number such as three or one hundred. When you multiply, you are scaling the measured number by a value that has no uncertainty, so the uncertainty and the significant figures stay tied to the measured value. For example, if you have two point five grams measured and you multiply by three exact items, the three is exact so the result keeps the two point five’s two significant figures and becomes seven point five grams. The exact count gives no extra precision because it did not come from a measurement that could vary.

Students sometimes treat exact counts as if they were measured and give the final answer too many significant figures; remember exact counts have infinite precision and do not add uncertainty, so keep the measured number of sig figs. Another common mistake is confusing exact conversion factors that are defined, like one dozen equals twelve, with measured equivalents like one cup equals two hundred thirty seven milliliters which can have uncertainty; use the defined exact ones to avoid losing or gaining sig figs. A short helpful tip is to always ask whether the number you are multiplying was measured or defined; if it was defined or counted exactly, do not change the measured value’s sig figs.

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Multiplying by Exact Counts and Sig Figs

1. Measured value determines precision
2. Exact counts have no uncertainty
3. Multiply scale without adding sig figs
4. Keep measured sig figs when multiplying
5. Exact counts do not increase precision

Common Sig Fig Mistakes with Counts

1. Treating exact counts as measured
2. Confusing defined conversions with measured ones
3. Giving final answers too many sig figs

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