Number of Significant Figures in Result of Division

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 $\dfrac m n$ can have is $\min \set {d_m, d_n}$.

Proof

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Examples

Significant Figures of $\dfrac {1 \cdotp 648} {0 \cdotp 023}$

$\dfrac {1 \cdotp 648} {0 \cdotp 023} = 72$

Sources

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