MHB Find Relative Error of A: 2.33

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The discussion focuses on calculating the relative error of the expression A = (317 + 0.3) - (171.499 + 145.501) with a base of 10 and a precision of 3. The initial calculation resulted in a relative error of 2.33, derived from the formula ||A - fl(A)|| / ||A||. However, it was later clarified that the correct calculation should use the values A = 0.3 and fl(A) = 1, leading to a relative error of 2.33 as well, but the user initially misstated the fraction as 7/5 instead of the correct 7/3. The final confirmation indicates that the calculations align, but the user acknowledges the error in notation. The discussion concludes with a resolution of the confusion regarding the relative error calculation.
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Hey! :rolleyes: I have also an other question :o
Suppose the base $\beta =10$ ,the precision $t=3$, $-L=U=10$ and $$A=(317+0.3)-(171.499+145.501)$$
I have to find the relative error for $A$.
We don't make rounding.For example,if we have the value $345.924$ it is equal to $0.345924*10^3$ and the corresponding floating number is $0.345*10^3$.
I found that it is equal to
$$\frac{||A-fl(A)||}{||A||}=\frac{7}{5}=2.33$$
Could you tell me if it is right?
 
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evinda said:
Hey! :rolleyes: I have also an other question :o
Suppose the base $\beta =10$ ,the precision $t=3$, $-L=U=10$ and $$A=(317+0.3)-(171.499+145.501)$$
I have to find the relative error for $A$.
We don't make rounding.For example,if we have the value $345.924$ it is equal to $0.345924*10^3$ and the corresponding floating number is $0.345*10^3$.
I found that it is equal to
$$\frac{||A-fl(A)||}{||A||}=\frac{7}{5}=2.33$$
Could you tell me if it is right?

I found that A=0.3 and fl(A)=1..
 
evinda said:
I found that A=0.3 and fl(A)=1..

Looks good! ;)... but doesn't that mean that:
$$\frac{||A-fl(A)||}{||A||} = \frac{|0.3 - 1|}{|0.3|} = \frac{0.7}{0.3} = 2.33$$

Oh wait! You also got $2.33$... while you shouldn't have. :eek: :rolleyes:
 
I like Serena said:
Looks good! ;)... but doesn't that mean that:
$$\frac{||A-fl(A)||}{||A||} = \frac{|0.3 - 1|}{|0.3|} = \frac{0.7}{0.3} = 2.33$$

Oh wait! You also got $2.33$... while you shouldn't have. :eek: :rolleyes:

I accidentally wrote $\frac{7}{5}$ :o I meant that it is equal to $\frac{7}{3}$..

Thank you very much! (Mmm)
 
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