Number of Significant Figures in Result of Addition or Subtraction/Examples/47.816 - 25

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Example of Use of Number of Significant Figures in Result of Addition or Subtraction

$47 \cdotp 816 - 25 = 22 \cdotp 816$

on the assumption that $25$ is exact.


Proof

We have that:

the least significant digit $d_m$ of $47 \cdotp 816$ is the $10^{-3}$ position
the least significant digit $d_n$ of $25$ is the $10^{-\infty}$ position.


So from Number of Significant Figures in Result of Addition or Subtraction:

the least significant digit of $47 \cdotp 816 - 25$ is the greater significant digit of $10^{-3}$ and $10^{-\infty}$, that is $10^{-3}$.


\(\ds 47 \cdotp 816 - 25\) \(=\) \(\ds 22 \cdotp 816\) by calculation
\(\ds \) \(=\) \(\ds 22 \cdotp 816\) to the nearest $10^{-3}$

$\blacksquare$


Sources