Frequently Asked Questions
How do I know if my answer is reasonable?
Always estimate first — round your inputs to nice numbers and calculate mentally or on scratch paper. If your calculator result is orders of magnitude different from your estimate, recheck your inputs for typos or unit errors. For most practical math, a result within 10% of your mental estimate is a good sanity check.
What's the difference between exact and approximate answers?
Exact answers are expressed in simplified form (e.g., √2, π/4, 3/7) without decimal approximation. Approximate answers round to a specified number of decimal places or significant figures. Use exact form when the problem asks for it; decimal approximations when a numerical result is needed for a real-world application.
Why does rounding matter in multi-step calculations?
Rounding intermediate results introduces small errors that compound through each calculation step — this is called rounding error or accumulated error. For best accuracy, keep full precision through all intermediate steps and only round the final answer. Most calculators do this automatically when you chain operations.
When should I use this type of calculation?
Check that your situation matches the assumptions behind the formula. Most mathematical models have specific domains of validity — ranges of input values where the model is accurate. Extrapolating beyond these ranges (e.g., applying a linear model to non-linear data) gives misleading results even when the formula is applied correctly.