Precise calculations are often impossible due to mathematical or informational limitations.  Estimates provide useful approximate answers, acting as a preliminary check for exact calculations; a significant discrepancy between an estimated and calculated result indicates an error.  Order-of-magnitude estimates, approximating values to the nearest power of 10, are sufficient for many problems.  Even crude estimates (within a factor of 10) offer valuable guidance; for example, estimating the number of people with a disease to within an order of magnitude can highlight significant public health concerns.  In making these estimates, rounding numbers significantly (e.g., π ≈ 1) is acceptable; for better accuracy, systematically balancing over- and underestimation is helpful, even when some quantities are unknown.