Number of Significant Figures in Result of Addition or Subtraction
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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
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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
- 1972: Murray R. Spiegel and R.W. Boxer: Theory and Problems of Statistics (SI ed.) ... (previous) ... (next): Chapter $1$: Computations