1989 AJHSME Problem 18

Many calculators have a reciprocal key \underline{\,\frac{1}{x}\,} that replaces the current number displayed with its reciprocal. For example, if the display is \underline{\,00004\,} and the \underline{\,\frac{1}{x}\,} key is pressed, then the display becomes \underline{\,000.25\,}. If \underline{\,00032\,} is currently displayed, what is the fewest positive number of times you must depress the \underline{\,\frac{1}{x}\,} key so the display again reads \underline{\,00032\,}?

\text{(A)}\ 1 \qquad \text{(B)}\ 2 \qquad \text{(C)}\ 3 \qquad \text{(D)}\ 4 \qquad \text{(E)}\ 5

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.