Rounding conventions in significant figures: When you encounter a trailing 5 during rounding (for example, 2.345 with three significant digits) and you drop the 5 instead of always rounding up, which specific rounding rule are you applying?

Introduction / Context:
Rounding is essential in measurements, reporting, and numerical computation. When a number sits exactly halfway between two representable values (the classic “. . . 5” case), different conventions yield different biases. The widely recommended technique for science and engineering is the round-to-even rule (also called bankers’ rounding), which minimizes systematic bias across large datasets.

Given Data / Assumptions:

• We are rounding a decimal quantity that has a trailing 5 followed by no further nonzero digits (for example, 2.345 rounded to three significant digits).
• The goal is to choose a rule that avoids bias in repeated rounding.
• We assume base-10 rounding and conventional significant-figure practices.

Concept / Approach:

In round-to-even, if the first discarded digit is exactly 5 and nothing follows (or the remaining digits are zeros), the retained last digit is adjusted to the nearest even number. This means sometimes you “drop the 5” (round down) and sometimes you round up, depending on whether the last retained digit is already even or odd. Over many numbers, upward and downward rounding occurrences balance, reducing drift in averages.

Step-by-Step Solution:

Verification / Alternative check:

A quick simulation on uniformly distributed half-way cases shows that round-to-even produces near-zero mean rounding error, whereas always-round-up yields a consistent positive bias. Many standards bodies and statistical texts recommend round-to-even for this reason.

Why Other Options Are Wrong:

• significant digit rule: A general concept describing how many digits to keep, not the specific half-way rule.
• round-off rule: Vague; could refer to any rounding convention.
• retained digit rule: Describes which digit is kept but not how to treat half-way values.
• truncate-toward-zero rule: Simply chops digits off; it does not implement unbiased half-way handling.

Common Pitfalls:

• Always rounding 5 up, which biases results.
• Confusing banker's rounding (round-to-even) with truncation.
• Forgetting that non-5 trailing digits follow the usual less-than-5 or greater-than-5 rules.

Final Answer:

round-to-even rule