Percent means divide by one hundred

Short answer: Percent to decimal: divide by 100. Decimal to percent: multiply by 100. Fraction to decimal: divide numerator by denominator. Fraction to percent: divide, then multiply by 100. Percent to fraction: place the percent over 100, clear any decimal, and simplify. Use decimal form for multiplication, percentage form for a requested rate, and exact fraction form when it prevents repeating-decimal rounding. One mortgage point is 1% of the loan amount, so 1.375 points becomes 0.01375. An increase from 6% to 6.5% is 0.5 percentage point, not a 0.5% relative increase. One basis point is one-hundredth of a percentage point. Always state the base because the same rate produces different dollar amounts when applied to sale price, loan amount, value, taxable EAV, or another total. Preserve the printed precision during working steps, then round only as directed. A calculator display without a label is unfinished work: 0.08 may mean a decimal rate, while 8% is the same value in the form the question may request. Make conversion visible. Write 4.5% = 0.045, label the base, and estimate 5% of that base. If the answer is supposed to be a rate, divide part by base first and convert the quotient back to percent only at the end. For a repeating fraction, retain the fraction or several guard digits rather than replacing one-third with 0.33. When two rates appear, ask whether they share a base. A 60% brokerage share followed by a 70% licensee share produces 42% of the original amount because the second percentage applies to the brokerage share. This routine catches decimal shifts, wrong denominators, premature rounding, and rates applied to the wrong subtotal before they reach the answer choices.

This page teaches numeric representation, not which real-world rate or base applies. Current tax, lending, compensation, valuation, and settlement facts come from official records, agreements, disclosures, and applicable rules. Illinois assessment examples require attention to county and property type; mortgage points use loan amount; actual lender pricing varies. The Department of Revenue says most Illinois property is assessed at 33 1/3% of fair market value, while Cook County classifications, farmland, and preferential assessments can differ. That makes one-third useful exam math, not a universal parcel assumption. The federal forms can use percentages, dollar amounts, or both, but a study conversion does not replace the disclosed term. Sources were checked through August 1, 2026.

1. Circle the printed form and the form required for the next operation or final answer. Write both labels so a bare calculator number cannot drift into the wrong form.
2. Convert percent to decimal by dividing by 100, decimal to percent by multiplying by 100, or fraction to decimal by division. Show the direction before moving the point.
3. Preserve exact fractions for one-third and other repeating values until the final step when practical. If decimal entry is necessary, carry enough digits to protect the final answer.
4. Name the base in words, such as loan amount for points or original value for percentage change. Do not let the largest number in the stem become the base automatically.
5. Use part = base x decimal rate, reversing with division when base or rate is unknown. Label the quotient before deciding whether to display it as decimal or percent.
6. For sequential percentages, write a new base before each rate is applied. A brokerage split, property-tax sequence, or successive value change may use a different base at every line.
7. Carry quoted precision and round only the final result according to the question. Keep an exact fraction available as a parallel check for repeating values.
8. Convert back, estimate magnitude, and check for a 100-times decimal-placement error. Also substitute the answer into the original relationship to see whether it recreates the given amount.

These questions are original study items aligned to the published outline. They are not copied, recalled, or predicted PSI questions.

Do not count recognition as mastery. Close the notes and explain the rule, apply it to a new fact pattern, and identify why each distractor fails.

• Use conversions inside the T-bar relationship
• Apply fractional percentages to mortgage points
• Apply exact rates to Illinois property-tax math
• Practice randomized percentage conversions

• PSI Illinois Candidate Information Booklet dated June 24, 2026
• Illinois Department of Revenue, current assessment and equalized-assessed-value guidance
• Consumer Financial Protection Bureau, current points and lender-credits explanation
• Federal Reserve, official glossary definition of a basis point
• Consumer Financial Protection Bureau, current Regulation Z Loan Estimate requirements
• National Institute of Standards and Technology, percent as the number 0.01

The current official outline controls the tested scope. Statutes, regulations, and official agency materials control when a general study rule and a jurisdiction-specific rule differ.