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Checking and Interpreting Results
Estimation catches major calculation mistakes, and understanding stated tolerances helps you read real data correctly.
Sanity-Checking an Answer
A quick estimate (rounding every number to significant figure, as in an earlier lesson) is one of the fastest ways to catch a major mistake — especially a misplaced decimal point or an extra zero, which a calculator will not warn you about.
Example 1 — catching a decimal-point slip
A student calculates and their calculator shows . Use an estimate to check whether this is reasonable.
- Estimate: round to significant figure:
- Compare: is about times larger than the estimate of
- This mismatch suggests a decimal point or digit was mistyped somewhere
The correct answer is — the student likely typed an extra .
Example 1 — reading a tolerance on a label
A food label states: "Contains ± mg of sodium." What does this mean?
- The ± mg is the tolerance — the amount the true value can vary by
- Lower bound:
- Upper bound:
Answer: The actual sodium content is anywhere from mg to mg.
Practice
More lessons in Numerical Precision, Accuracy and Errors · Next: Course Exam · Previous: Error in Real Problems