Apply a $$stepwise refinement approach$$ to develop three different levels of procedural abstractions for one or more of the following programs:

Develop a check writer that, given a numeric dollar amount, will print the amount in words normally required on a check.

Iteratively solve for the roots of a transcendental equation.

Develop a simple task$-$scheduling algorithm for an operating system.

Write an algorithm in Python that will represent your stepwise refinement approach for the program of your choice.