Rounding Off — Fundamental Concepts

Fundamental Concepts

Specify the retained place

Rounding 47.386 to two decimal places gives 47.39 under the ordinary school convention. Rounding to the nearest ten gives 50. Decimal places count positions after the decimal point; significant figures count from the first nonzero digit. These instructions can therefore produce different results for the same number.

Round once when possible

For 2.449, direct rounding to one decimal place gives 2.4. Rounding first to two decimal places gives 2.45, which then rounds to 2.5 at one decimal place. This double-rounding error arises because the intermediate result loses information. Keep extra digits through the calculation and round the final output.

Use bounds for reported values

If a positive measurement is reported as 18 to the nearest whole unit, the original value lies from 17.5 inclusive to 18.5 exclusive under half-up rounding. It is not known to equal exactly 18. Combining rounded measurements may therefore require an interval rather than a single exact sum.

Match approximation to the decision

Rounding 398 × 21 to 400 × 20 gives a quick estimate near 8,000. That may distinguish widely separated options but not close alternatives. If an answer lies near a threshold, calculate more accurately or use error bounds. Approximation is useful when its precision is sufficient for the question, not simply because it is faster.