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Suppose that $x$ is the exact value of some quantity and $\hat{x}$ is the approximate value of this quantity. The numbers $$\Delta(\hat x):=|x-\hat x|,$$ $$\delta(\hat x):=\frac{\Delta(\hat x)}{|\hat x|}$$ are called absolute and relative errors, respectively.

For example, the Gravitational constant is $G=(6,67259\pm0,00085)\times 10^{-11} $.

My book says that in this example relative errors does not exceed $13\times 10^{-5}$ .

Can anyone clarify it please? The question seems really stupid but anyway I'd be thankful for clarification!

RFZ
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1 Answers1

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The approximated value of $G$ is $6.67259\times 10^{-11}$, but the real value could be anything in the interval $[6.67174\times 10^{-11},6.67344\times 10^{-11}]$. You do no really know it, but the maximum absolute error would be achieved when it is one of the endpoints. Therefore, the maximum relative error is: $$\delta(\hat x)=\frac{\Delta(\hat x)}{|\hat x|}=\frac{0.00085\times 10^{-11}}{6.67259\times 10^{-11}}\approx13\times 10^{-5}$$

AugSB
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