Calculate the absolute and relative errors in $a+5b/c-3b\cdot c$ where $a=3.5435$, $b=0.2588$, $c=1.0150$ are correct up to 4 decimal places.

Question

I only know how to find the absolute and relative errors when, let say $a=0.123$ and $b=12.37$.

I first of all computed the maximum absolute error using rounding and in base 10. And use it to compute the relative error.

But I don't know how to go about this one.

Answer 1

You must consider each piece separataly.

Say $$A=\frac b c\implies \frac{\Delta A} A=\frac{\Delta b} b+\frac{\Delta c} c\implies\frac{\Delta A} A=???\implies\Delta A=???$$ $$B= b c\implies \frac{\Delta B} B=\frac{\Delta b} b+\frac{\Delta c} c\implies\frac{\Delta B} B=???\implies\Delta B=???$$

Now $$\Delta \left(a+5\frac b c-3b c\right)=\Delta a+5\Delta A+3\Delta B$$ $$\frac{\Delta \left(a+5\frac b c-3b c\right)}{a+5\frac b c-3b c}=\frac{\Delta a+5\Delta A+3\Delta B }{a+5\frac b c-3b c}$$