Number of Significant Figures in Result of Addition or Subtraction

From ProofWiki
Jump to navigation Jump to search

Theorem

Let $m$ and $n$ be numbers.

Let $d_m$ and $d_n$ be the position of the least significant digit of $m$ and $n$ respectively.


Then the least significant digit in either $m + n$ or $m - n$ is in the position corresponding to the greater significant digit of $d_m$ and $d_n$.


Proof


This theorem requires a proof.
In particular: I need a run-up.
You can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by crafting such a proof.
To discuss this page in more detail, feel free to use the talk page.
When this work has been completed, you may remove this instance of {{ProofWanted}} from the code.
If you would welcome a second opinion as to whether your work is correct, add a call to {{Proofread}} the page.


Examples

Significant Figures of $3 \cdotp 16 + 2 \cdotp 7$

$3 \cdotp 16 + 2 \cdotp 7 = 5 \cdotp 9$


Significant Figures of $83 \cdotp 42 - 72$

$83 \cdotp 42 - 72 = 11$


Significant Figures of $47 \cdotp 816 - 25$

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

on the assumption that $25$ is exact.


Sources

Retrieved from "https://proofwiki.org/w/index.php?title=Number_of_Significant_Figures_in_Result_of_Addition_or_Subtraction&oldid=549311"