Number of Significant Figures in Result of Multiplication

Theorem

Let $m$ and $n$ be numbers which are presented to $d_m$ and $d_n$ significant figures respectively.

Then the most significant figures that $m \times n$ can have is $\min \set {d_m, d_n}$.

Proof

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Examples

Significant Figures of $73 \cdotp 24 \times 4 \cdotp 52$

$73 \cdotp 24 \times 4 \cdotp 52 = 331$

Significant Figures of $8.416 \times 50$

$8 \cdotp 416 \times 50 = 420 \cdotp 8$

on the assumption that $50$ is exact.

Sources

• 1972: Murray R. Spiegel and R.W. Boxer: Theory and Problems of Statistics (SI ed.) ... (previous) ... (next): Chapter $1$: Computations