The geometric series can be used to approximate the reciprocal of a number by using a nearby number whose reciprocal is known. For example, $\displaystyle \frac1{24} = \frac1{25}\frac1{1-\frac1{25}}$ =
$\displaystyle \frac1{25} \sum_{n=0}^{\infty} \left( \frac1{25} \right) ^n$
leads to the approximation $\displaystyle \frac1{25}\left(1 + \frac{1}{25}\right)$ of $\displaystyle \frac1{24}$ by truncating the series.
This approximation to $\displaystyle \frac{1}{24}$ is easily expressed as a decimal: $.04(1+.04) = .0416.$
Use the fact that 94 is near 100 to get a similar four place decimal approximation of $\displaystyle \frac1{94}.$

The error in approximating a number A by a number a is e = a-A. The relative error is e/A. The relative percent error is 100e/A.
Find the relative percent error in the approximation of $\frac{1}{94}$ described above.