Number of Significant Figures in Result of Multiplication/Examples/8.416 x 50

Example of Use of Number of Significant Figures in Result of Multiplication

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

on the assumption that $50$ is exact.

Proof

We have that:

the number of significant figures $d_m$ in $8 \cdotp 416$ is $4$

the number of significant figures $d_n$ in $50$ is unlimited

So from Number of Significant Figures in Result of Multiplication:

the number of significant figures in $8 \cdotp 416 \times 50$ can be no more than $\min \set {4, \infty}$, that is $4$.

\(\ds 8 \cdotp 416 \times 50\)

\(=\)

\(\ds 420 \cdotp 8\)

by calculation

\(\ds \)

\(=\)

\(\ds 420 \cdotp 8\)

to $4$ significant figures

$\blacksquare$

Sources

• 1972: Murray R. Spiegel and R.W. Boxer: Theory and Problems of Statistics (SI ed.) ... (previous) ... (next): Chapter $1$: Computations: Example 4.