Illinois real estate exam math

Real estate math rounding rules

Keep intermediate results unrounded, then round the final answer to the unit and precision requested. Follow any explicit question, form or table instruction first. A partial Illinois transfer-tax unit uses a ceiling, so even a small fraction can require the next whole unit.

Last reviewed: October 24, 2026

When should you round a real estate math answer?

For ordinary practice calculations, carry precision until the last step unless instructed otherwise. Read the requested unit before you start. A correct formula can still produce the wrong answer if you report dollars instead of cents or a decimal rate instead of a percentage.

Choose the rule from the question
Instruction	What to do	Example or caution
Nearest cent	Finish the calculation, then retain two decimal places.	$18,437.286 becomes $18,437.29.
Nearest whole dollar	Retain no cents; use the stated tie rule when exactly halfway.	$18,437.286 becomes $18,437.
Percentage to two decimal places	Convert the full decimal quotient to percent before rounding.	0.086543 becomes 8.65%, not 0.09%.
Proration	Keep the daily quotient through multiplication; round the requested final share.	Use the day-count method supplied in the problem.
Acreage to three decimal places	Divide square feet by 43,560, then round the acreage.	100,000 square feet becomes 2.296 acres.
Per $500 or fraction thereof	Count every partial $500 block as one full unit.	600.002 units requires 601 units; exactly 600 stays 600.
Named form or table instruction	Use the instruction for that field or calculation.	A required intermediate rounding step overrides the general study method.

The PSI booklet does not supply a universal rounding rule for every Illinois exam problem. The method on this page is study advice. An explicit instruction in the question takes priority.

A simple order that prevents early rounding

Mark the answer unit. Cents, whole dollars, percent, acres or taxable units?
Set up the relationship. Keep quoted rates and exact fractions intact. For example, 2.75% is 0.0275, while exact one-third is not 0.33.
Complete the arithmetic. Use the carried calculator result rather than retyping a shortened display. Where possible, keep a fraction such as 7,100 ÷ 365 in the expression.
Apply the requested rule once at the end. For ordinary nearest rounding, find the retained place. A next digit below 5 leaves it unchanged; above 5 raises it. A 5 with a later nonzero digit is above halfway and also raises it. Handle an exact halfway value under the stated convention.
Check the size and label. A 7.30% cap rate should not become 0.07% because you forgot the percentage conversion.

A carry can cross a dollar boundary: exactly $9.995 becomes $10.00 to cents under half-up. Keep both decimal places when the answer asks for cents.

Rounding twice can also change a result. Exactly 4.4449 rounded directly to two decimal places is 4.44. Rounding it to 4.445 first and then applying half-up to two places gives 4.45. Start from the original value when rounding the final answer.

Why rounding a daily proration rate too soon costs cents

Assume annual tax of $7,100, a supplied 365-day divisor and a party responsible for 200 days. The problem asks for the final share to the nearest cent and gives no instruction to round the daily rate.

Carry the quotient through the multiplication

$7,100 ÷ 365 × 200 = $3,890.4109589…

Final share: $3,890.41.

Rounding the daily rate first to $19.45 gives $19.45 × 200 = $3,890.00. That is $0.41 less.

If a problem expressly requires a daily rate rounded to cents, follow that instruction instead. This example assumes the 200 days are already established. Choosing the divisor, counting the closing day and deciding whose debit or credit applies are separate tasks. Review 360 vs. 365-day proration for those choices.

Worked examples: money, rates, acres and taxable units

Each answer below follows its stated format. The calculations are original examples, with exact inputs supplied for practice.

Round after the calculation, using the requested unit
Calculation	Setup	Final answer	Why it matters
Commission	$375,000 × 0.0275	$10,312.50	A 2.75% rate is 0.0275. A neat half-dollar does not remove the cents when cents are requested.
Capitalization rate	$67,500 ÷ $925,000 × 100	7.30% to two decimal places	The unrounded percentage is about 7.297297%. Rounding the decimal quotient to 0.07 first loses information.
Acreage	100,000 ÷ 43,560	2.296 acres to three decimal places	The quotient is about 2.295684. These are supplied exam measurements, not a survey accuracy claim.
Exact fraction	$500,000 ÷ 3	$166,666.67 to the nearest cent	Using 0.33 instead of exact one-third gives $165,000, which changes the calculation rather than just its final format.
Illinois state transfer tax	Ceiling of ($300,001 ÷ $500), then × $0.50	$300.50 for the state component	Use 601 units. The taxable value is already supplied; county or municipal tax is not included.

For the transfer-tax example, $300,001 is already the taxable amount after any required adjustments. Use 601 units for the state calculation. An exact $300,000 would use 600 units, not 601. Actual county and municipal components require their own applicable rates; the state answer alone is not the total closing tax.

See Illinois transfer-tax math for the broader calculation and percent, decimal and fraction conversions if the rate setup is the part you missed.

When does a form require a different rounding method?

A named form rule controls its own fields. Do not turn the general advice to carry precision into a rule that overrides an explicit form instruction.

Illinois PTAX-203: Step 2 of the current form directs upward rounding of its specified dollar entries to whole dollars. Line 18 separately rounds the $500 unit count upward. Lines 19 and 20 apply the state and county stamp rates. Use the actual form instructions when completing those entries.
Loan Estimate: 1026.37(o)(4) requires whole dollars for listed fields, with exceptions. Its interpretation also distinguishes totals calculated from required rounded components from totals using unrounded components.
Closing Disclosure: 1026.38(t)(4) has its own whole-dollar exceptions and three-decimal treatment for specified percentages, with trailing zeros dropped. Other amounts use exact numerical disclosure with decimal places where applicable.

These examples explain why the field matters. They are not a complete mortgage-disclosure or tax-filing checklist. In a practice question, use the form, field and instruction actually named.

Does a 5 always round up?

Not under every convention. Exactly $12.345 becomes $12.35 under half-up and $12.34 under half-to-even. With half-to-even, an exact tie keeps an even last retained digit. The NIST guidance describes that convention in its scientific measurement context; it is not an Illinois exam mandate.

A number such as $12.3451 is above the halfway point and becomes $12.35 under both methods. Our tie-sensitive practice question names its convention so you are tested on applying a rule rather than guessing an unstated one.

Six real estate math rounding practice questions

Choose an answer before opening the explanation. Each original question explains all four choices and shows how one changed instruction affects the result. These are not actual PSI items.

1. Read the requested place

A completed commission calculation is $2,718.286. The question asks for the nearest cent. Which answer follows that instruction?

$2,718.28
$2,718.29
$2,718.30
$2,718

Show answer and explanations

Answer: B. $2,718.29

Why this misses: That drops the third decimal without rounding. The discarded 6 requires the retained hundredths digit to increase.
Correct. Keep two decimal places. The third decimal is 6, so 28 cents becomes 29 cents.
Why this misses: That rounds to a tenth of a dollar and adds a zero. The question requests hundredths of a dollar.
Why this misses: That is the nearest whole dollar, not the nearest cent.

Change the facts: If the question instead asks for the nearest whole dollar, the answer is $2,718. The formula has not changed; the requested reporting place has.

Source: Appendix B.7.1; original non-tie arithmetic example

2. Carry the daily rate

Annual tax is $7,100. A problem assigns one party 200 days, specifies a 365-day method and asks for the final share to the nearest cent. It gives no intermediate rounding instruction. What is the share?

$3,890.00
$3,944.44
$3,890.42
$3,890.41

Show answer and explanations

Answer: D. $3,890.41

Why this misses: This comes from rounding the daily quotient to $19.45 before multiplying by 200. The final share is understated by $0.41.
Why this misses: This uses 360 as the divisor. The problem expressly supplies 365.
Why this misses: The unrounded share is about $3,890.410959. Its third decimal is 0, so rounding does not raise 41 cents to 42.
Correct. Calculate $7,100 ÷ 365 × 200 without rounding the daily result. Round the completed share to cents.

Change the facts: If the problem explicitly requires the daily rate to be rounded to cents first, use $19.45 × 200 = $3,890.00. Follow that stated method even though it differs from the general study approach.

Source: National XI.A.3, real property tax and other prorations; original calculation under supplied assumptions

3. Convert to percent first

A property has annual net operating income of $67,500 and a value of $925,000. What is its capitalization rate, expressed as a percentage to two decimal places?

7.30%
7.00%
0.07%
7.29%

Show answer and explanations

Answer: A. 7.30%

Correct. Divide NOI by value, then multiply by 100: about 7.297297%. The third decimal is 7, so 7.29% rounds to 7.30%.
Why this misses: This can result from rounding the decimal quotient to 0.07 too soon. Preserve it through the percentage conversion.
Why this misses: This reports a rounded decimal quotient as though it were already a percentage. Multiplying by 100 is missing.
Why this misses: This truncates the percentage at two decimal places instead of rounding it.

Change the facts: If the requested answer is a decimal rate to four decimal places, report 0.0730. A decimal rate and a percentage have different displayed values and units.

Source: National XI.B.2, rate of return/capitalization rate; original calculation

4. A partial unit counts

An Illinois example supplies $300,001 as net consideration subject to transfer tax and asks only for the state component at $0.50 per $500 or fraction thereof. What is due?

$300.00
$300.001
$300.50
$450.75

Show answer and explanations

Answer: C. $300.50

Why this misses: This uses 600 units and ignores the remaining $1. A partial $500 unit must count.
Why this misses: This multiplies the fractional unit count directly by $0.50. The rule requires whole taxable units, not a fractional tax calculation.
Correct. $300,001 ÷ $500 = 600.002. Use 601 units, then multiply by $0.50.
Why this misses: This combines $0.50 state and $0.25 county rates for 601 units. The question asks for the state component only.

Change the facts: If the supplied taxable value is exactly $300,000, there are exactly 600 units and the state component is $300.00. A ceiling does not add a unit to an exact multiple.

Source: PTAX-203, Step 2, lines 18-19; original taxable-value example

5. Use the named tie convention

A practice question expressly says to use round-half-up. What is exactly $12.345 rounded to the nearest cent under that instruction?

$12.34
$12.35
$12.345
$12.30

Show answer and explanations

Answer: B. $12.35

Why this misses: This would be the result under half-to-even, since the retained 4 is even. The question expressly requires half-up.
Correct. The amount is exactly halfway between $12.34 and $12.35. Under the specified half-up method, choose $12.35.
Why this misses: That preserves three decimal places rather than answering to the nearest cent.
Why this misses: That rounds to one decimal place, not to two.

Change the facts: Under an expressly required half-to-even convention, exactly $12.345 becomes $12.34. The number $12.3451 is above halfway and rounds to $12.35 under either convention.

Source: Appendix B.7.1; contrast with the explicitly supplied half-up convention

6. Recognize when the general method stops

A question specifically concerns a Loan Estimate subtotal whose component amounts are themselves required to be rounded under the applicable rule. Which approach follows the official interpretation?

Always total unrounded amounts, regardless of the form instruction.
Round every mortgage figure and percentage to a whole number.
Use the rounding method from a different disclosure because all mortgage forms match.
Calculate that subtotal from the required rounded component amounts.

Show answer and explanations

Answer: D. Calculate that subtotal from the required rounded component amounts.

Why this misses: Preserving precision is useful study advice, but it does not override a rule expressly requiring the total to use rounded components.
Why this misses: The regulation has field-specific exceptions and percentage rules. It does not impose whole-number presentation on every entry.
Why this misses: Loan Estimate and Closing Disclosure requirements are not interchangeable.
Correct. The official interpretation distinguishes totals using components required to be rounded from totals using components not required or permitted to be rounded.

Change the facts: If the rounded total instead uses components not required or permitted to be rounded, the interpretation calls for those unrounded components in the calculation, followed by the required total rounding.

Source: 1026.37(o)(4), official interpretation 2, Calculations

Real estate math rounding FAQ

Does PSI publish one rounding rule for every Illinois exam calculation?

The June 24, 2026 Illinois booklet reviewed for this page does not state one universal rounding or tie-breaking rule. Read the actual question and any supplied table or instructions. Keeping intermediate precision is study guidance here, not a quoted PSI policy.

Should I round every money calculation to two decimal places?

No. If the final answer asks for cents, use two decimal places. Keep intermediate results through the later steps unless an instruction requires otherwise. A request for whole dollars or a named form rule can require a different approach.

Do I round a proration daily rate first?

Usually preserve the daily quotient for the multiplication in a practice problem with no contrary instruction. The final share is then rounded as requested. If the problem explicitly requires a rounded daily rate, follow it. Whether to use 360, 365 or a supplied calendar method is a separate question.

Do I round a cap rate before multiplying by 100?

Keep the quotient, multiply by 100 to express it as a percentage, then round to the requested places. For example, 0.07297297 is about 7.297297%, which becomes 7.30% to two decimal places. Two decimal places is not the same instruction as two significant figures.

Does or fraction thereof mean round up?

For a positive transfer-tax unit count, yes: count any remaining part of a unit as one more unit. Exactly 600 units stays 600; 600.002 requires 601. Establish the taxable value first and apply the rate for the component actually requested.

What if a calculator or spreadsheet gives a different answer at 5?

An exact halfway value can be treated differently under half-up and half-to-even. Software can also represent some decimal inputs approximately. Check the original number and named convention rather than treating a displayed last digit as proof. This page states the tie rule whenever a practice answer depends on it.

What if the problem gives no rounding instruction?

Keep precision while solving, preserve the correct units and compare your result with the choices. Cents are a useful reporting choice for ordinary practice money answers, not a universal provider rule. If two choices differ only because of an unstated exact tie convention, the practice question needs clarification.

Are these real PSI exam questions?

No. These are original teaching questions. The national Real Estate Calculations area is 7% of the broker outline in the reviewed booklet; it does not promise a separate rounding question count. A score on these six items is not a validated readiness measure.

What to practice next

Try the real estate math drill. When you miss an answer, identify whether the error came from the formula, units, a shortened intermediate result or the final instruction. Work that step again before starting another set.

If you prefer short sessions on your phone, you can download Pass Illinois and use the explanations to revisit the calculation you missed.

Sources and October 2026 review

Reviewed October 24, 2026. PSI's national XI: Real Estate Calculations area covers 7% of the broker outline. Rounding supports those calculations; there is no separate promised rounding quota. The June 24 booklet and current IDOR and CFPB sources were checked alongside the original arithmetic. The table examples do not establish an actual property's taxable value or a lender's disclosure obligations.

Source publication and form revision dates are different from this review date. Follow the actual question and supplied instructions on an exam, and current governing rules for a real transaction.

How we review and correct content