Explained clearly 5 min read

Which Tie-Breaking Rule Do AP Chemistry, IB, and High School Teachers Expect?

AP Chemistry and most US high school teachers expect round-half-up for exact 5 ties; IB sciences and international metrology standards typically expect round-half-to-even. A 5 followed by a nonzero digit is never a tie.

Written by Tommy C. MoranPublished November 14, 2026

Short Answer

Quick Facts

AP Chemistry tie-breaker	Round-half-up is the dominant US classroom expectation; the AP CED does not specify a tie-breaking rule.
IB tie-breaker	IB sciences often expect round-half-to-even, aligned with ISO 80000-1 and ASTM E29.
Exact tie definition	A tie occurs only when the first discarded digit is 5 and all following discarded digits are zero.
5 followed by nonzero	Not a tie; round up under both half-up and half-even rules.
ASTM E29-22	Section 6.2 specifies round-half-to-even for conformance testing.
ISO 80000-1:2009	Clause 7.3.3 specifies round-half-to-even for exact 5 ties.
Software variation	Excel ROUND uses half-away-from-zero; Python Decimal can use ROUND_HALF_EVEN; calculators may differ.
Double rounding	Rounding intermediate results can change the final answer; round once at the end.

The tie-breaking rule for significant figures is the rule that applies when the digit immediately after the last retained digit is exactly 5 and no nonzero digits follow. This is not the same as the common 5 or more, round up rule. AP Chemistry and most US high school teachers expect round-half-up for exact ties. IB sciences and international metrology standards typically expect round-half-to-even, sometimes called banker’s rounding. This reference explains expectations, standards, and pitfalls.

Rule Statement

An exact tie occurs only when the first discarded digit is 5 and all subsequent discarded digits are zero. For example, 2.45 rounded to two significant figures is a tie; 2.4501 is not. The two main tie-breakers are:

Round half up (half away from zero): Increase the last retained digit by 1. For positive values, 2.45 becomes 2.5. For negative values, -2.45 becomes -2.5 if the convention is half away from zero.
Round half to even: Round to the nearest even last retained digit. For 2.45 to two significant figures, the retained digit 4 is even, so it stays 4: 2.4. For 2.55 to two significant figures, the retained digit 5 is odd, so it becomes 6: 2.6.

AP Chemistry: The College Board AP Chemistry Course and Exam Description does not publish a separate tie-breaking clause. US textbooks and AP teachers overwhelmingly use round-half-up. Exact ties are rare on the AP exam, and scoring usually focuses on correct significant-figure counts rather than a single tie-breaker.

IB: IB Chemistry and other IB sciences often align with ISO 80000-1 and ASTM E29, which specify round-half-to-even. Always check the current subject guide and your teacher’s IA feedback, because some IB teachers still use half-up.

High school teachers: Most US high school chemistry and physics teachers expect round-half-up, following the textbook rule if the digit after the last significant figure is 5 or greater, round up.

Convention Comparison Table

Context	Expected tie-breaker	2.45 to 2 SF	Notes
AP Chemistry / US high school	Round half up	2.5	Common in Brown/LeMay, Zumdahl, and most US classrooms. College Board does not specify a tie-breaker.
IB Chemistry / IB sciences	Round half to even	2.4	Often aligned with ISO 80000-1 and ASTM E29. Check current subject guide.
General high school (US)	Round half up	2.5	Textbook rule: 5 or more, round up.
ASTM E29-22	Round half to even	2.4	Section 6.2 for conformance testing.
ISO 80000-1:2009	Round half to even	2.4	Clause 7.3.3.
NIST SP 811	Round half to even	2.4	Section 7.8.
Software	Varies	Python Decimal: 2.4; Excel ROUND: 2.5	Floating-point can obscure exact ties; verify library behavior.

Worked Examples

Example 1: 2.45 to two significant figures

This is an exact tie because the first discarded digit is 5 and there are no nonzero digits after it.

AP/US high school: last retained digit 4, exact 5, round up -> 2.5.
IB/ISO/ASTM: last retained digit 4 is even, keep it -> 2.4.

Example 2: 2.4501 to two significant figures

Not a tie. The 5 is followed by 01, so the value is greater than half. Both conventions round up -> 2.5.

Example 3: 2.55 to two significant figures

Half-up: 2.6.
Half-even: retained 5 is odd, round up -> 2.6.

Example 4: 2.25 to two significant figures

Half-up: 2.3.
Half-even: retained 2 is even, keep it -> 2.2.

Example 5: -2.45 to two significant figures

For half-away-from-zero, common in US schools, -2.45 -> -2.5. For half-even, -2.45 -> -2.4. Always state whether negative numbers round away from zero or toward positive infinity.

Counter-Examples

Treating 2.4501 as an exact tie. The nonzero after 5 makes it greater than half. Round up: 2.5 under both rules.
Double rounding. 2.4445 to three significant figures is 2.44, because the fourth significant digit is 4. If you first round to 2.445 and then to 2.44 or 2.45, you may introduce a double-rounding error.
Rounding before all operations. Keep extra digits through the calculation and round once at the end.
Mixing decimal places and significant figures. 12.25 to three significant figures is not the same as 12.25 to two decimal places.
Assuming every calculator uses half-even. TI-84 display, Excel ROUND, Python round, and Python Decimal can differ.

Standards Citation

For metrology, conformance, and uncertainty reporting, the dominant tie-breaker is round-half-to-even:

ASTM E29-22, Standard Practice for Using Significant Digits in Test Data to Determine Conformance with Specifications, Section 6.2: ties round to the nearest even digit.
ISO 80000-1:2009, Quantities and units — Part 1: General, Clause 7.3.3: exact 5 ties round to the nearest even retained digit.
NIST SP 811, Guide for the Use of the International System of Units (SI), Section 7.8: recommends round-half-to-even for exact ties.
JCGM 100:2008 (GUM), Clause 7.2.2: gives guidance on rounding uncertainty values; it is not a tie-breaker but is central to precision reporting.

AP and IB are educational assessment contexts, not metrology standards. The AP Chemistry CED does not contain a tie-breaking clause. IB subject guides often point to ISO-style rounding, but exact exam marking can vary by subject and year.

Common Mistakes

Applying half-even to every digit 5, even when followed by nonzero digits.
Double rounding: rounding intermediate results and then rounding again.
Counting leading zeros as significant in numbers like 0.004565.
Forgetting that exact numbers, such as counted objects and defined conversions, do not limit significant figures.
Using a calculator’s display rounding as a substitute for significant-figure reasoning.
Not clarifying negative-number behavior.

Quick Reference Table

Value to round	Target	Half-up	Half-even	Notes
2.45	2 SF	2.5	2.4	Exact tie; retained 4 is even.
2.55	2 SF	2.6	2.6	Retained 5 is odd; both round up.
2.4501	2 SF	2.5	2.5	Not a tie; 5 is followed by nonzero.
2.25	2 SF	2.3	2.2	Exact tie; retained 2 is even.
-2.45	2 SF	-2.5	-2.4	Clarify negative-number convention.

Practice Problems

Round 12.25 to three significant figures under half-up and half-even.
Round 12.35 to three significant figures under half-up and half-even.
Round 0.004565 to two significant figures under both rules.
Round 45.45 to three significant figures under both rules.

Answers: 1. Half-up 12.3; half-even 12.2. 2. Both 12.4. 3. Both 0.0046; the 5 is followed by 6, so it is not a tie. 4. Half-up 45.5; half-even 45.4; retained 4 is even.

This site is a precision-and-rounding reference, not just a calculator. The calculator is accurate, but the rules, standards, and pitfalls above are the core educational value.

FAQ

Does AP Chemistry require banker's rounding?

No. The AP Chemistry Course and Exam Description does not specify a tie-breaker. US textbooks and AP teachers typically expect round-half-up for exact 5 ties, and exact ties are uncommon on the exam.

Does IB use round-half-to-even?

IB sciences often align with ISO 80000-1 and ASTM E29, which use round-half-to-even. However, some IB teachers accept or teach half-up, so check your current subject guide and IA feedback.

What if the 5 is followed by a nonzero digit?

Then it is not a tie. Round up under both half-up and half-even. For example, 2.4501 to two significant figures is 2.5.

Why do calculators disagree on rounding?

Different software uses different tie-breakers. Excel ROUND uses half-away-from-zero; Python Decimal can use ROUND_HALF_EVEN; TI-84 display behavior may differ. Binary floating-point can also make an exact decimal tie appear slightly above or below 0.5.

Which rule should I use on a high school exam?

Use the rule your teacher specifies. If none is given, use round-half-up for AP and most US high school courses, and round-half-to-even for IB and metrology or engineering standards.