Calculating relative error I am struggling with a task I've been given. I've been given only basic information about the relative error and it doesn't seem to be enough to help me solve the following problem: I'm supposed to determine relative error of $q$,
$$q=\frac {aC}{1+bC}$$
Where $C$ is from interval $[10^{-4},0.1]$ and $C$ has a relative error 3% (minimum $2*10^{-5}$) .
$$ a=1, b=1 $$ and both $a$ and $b$ have relative error 10% .
 A: One trick to compute relative error is this formula:
$$
d\log f=\frac{df}{f}
$$
Hence relative error for $q$ can be computed as follows:
\begin{align*}
d\log q &= d\log a+d\log C-d\log(1+bC) \\
&=\frac{da}{a}+\frac{dC}{C}-\frac{bdC+Cdb}{1+bC} \\
&=\frac{da}{a}+\frac{dC}{C}-\frac{\frac{dC}{C}+\frac{db}{b}}{1+\frac{1}{bC}} \\
&=\frac{da}{a}+\left(1-\frac{bC}{1+bC}\right)\frac{dC}{C}-\left(\frac{bC}{1+bC}\right)\frac{db}{b}
\end{align*}
So, your relative error for $q$ is:
$$
\frac{\Delta q}{q}=\frac{\Delta a}{a}+\left(\frac{1}{1+bC}\right)\frac{\Delta C}{C}-\left(\frac{bC}{1+bC}\right)\frac{\Delta b}{b}
$$
I let you do the numerical application

Some clarifications:
Let the true value of a quantity be $x$￼ and the measured or inferred value ￼$\tilde{x}$. Then the relative error $\delta x$ is defined by
$$
\delta x=\frac{\Delta x}{x}=\frac{|\tilde{x}-x|}{x}
$$
where $\Delta x=|\tilde{x}-x|$ is the absolute error
For instance if $a=2$ with a relative error error of $3\%$ you have
$$
0.03=\frac{\Delta a}{2} \Rightarrow \Delta a=0.06 \Rightarrow \tilde{a}\in[1.94,2.06]
$$
Now if you want to compute the relative error $\delta q$, using $\delta a=10\%$ around $a=1$, $\delta b=10\%$ around $b=1$ and $\delta C=3\%$
$$
\delta q = \frac{\Delta q}{q} = 0.1+0.03\left(\frac{1}{1+C}\right)-0.1\left(\frac{C}{1+C}\right)=\frac{0.13}{1+C}
$$
Now, it is true that it is strange to give an interval for $C$ values (usually one give a point $(a,b,C)\in\mathbb{R}^3$ and given small variations, aka our relative errors, $(\delta a,\delta b,\delta C)\in\mathbb{R}^3$, we compute the varation of the output function, our $\delta q$.
To continue I assume that $\delta C=3\%$ is constant for $C\in[10^{-4},0.1]$ and compute the corresponding values for $\delta q$. You get:
$$
\delta q\in [0.118182, 0.129987]
$$
This is my suggestion.

Another thing, in your question, I do not understand " minimum $2\times 10^{-5}$ "
