3. The number $x$ has the following property: subtracting $\frac{1}{10}$ from $x$ gives the same result as multiplying $x$ by $\frac{1}{10}$. What is the number $x$ ?
A $\frac{1}{100}$
B $\frac{1}{11}$
C $\frac{1}{10}$
D $\frac{11}{100}$
E $\frac{1}{9}$
SOLUTION
$\mathbf{E}$

From the information given in the question we see that $x$ satisfies the equation $x-\frac{1}{10}=\frac{x}{10}$. Multiplying both sides by 10 gives $10 x-1=x$, so $9 x=1$. So $x=\frac{1}{9}$.