Problem

Determine the appropriate precision for the product of measurements \(3.2~m\) and \(4.15~m\). State the precision rule and its justification.

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Multiplication uses significant digits rather than matching decimal places. Count the meaningful digits in each measured factor, let the smallest count limit the product, and keep the calculator value unrounded until the end so intermediate rounding does not introduce avoidable error.

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Use the tenths place because 3.2 is measured to the tenths place, so the product should match that decimal place.

Use 5 significant digits because 3.2 and 4.15 together have 5 significant digits in the calculation.

Use 2 significant digits because 3.2 has 2 significant digits, which is the fewest in the multiplication.

Use 3 significant digits because 4.15 has 3 significant digits, so the product should keep the greater precision.

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Determine the appropriate precision for the product of measurements \(3.2~m\) and \(4.15~m\). State the precision rule and its justification.

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