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HESI A2 Math study materials
HESI A2 Math study resources

HESI A2 Math: Decimals, Percentages, and Proportions

HESI A2 Math · Work through your exam, one topic at a time.

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Decimals, Percentages, and Proportions

The Decimals, Percentages, and Proportions domain checks fluency converting among decimals, fractions, and percents, solving percent equations, and setting up proportions correctly. HESI-style items often pair these skills with a clinical scenario, such as a dosage or solution strength, so the arithmetic must be right and the units must line up.

Decimals

Line up decimal points when adding or subtracting; count total decimal places when multiplying; move the decimal point in both divisor and dividend before dividing. To round, look at the digit immediately to the right of the target place: 5 or more rounds up.

Converting and computing percents

  • Percent to decimal: divide by 100 (15% = 0.15; 7.5% = 0.075).
  • Decimal to percent: multiply by 100.
  • Fraction to percent: divide numerator by denominator, then multiply by 100.
  • Core equation: part = percent × whole. Rearranged: whole = part ÷ percent; percent = part ÷ whole.
  • Percent change = amount of change ÷ original amount × 100.

Proportions

A proportion states that two ratios are equal: a/b = c/d. Cross-multiply to get ad = bc, then divide. Write both ratios with the same units in the same positions - milligrams over milliliters on both sides, for example. Labeling units before cross-multiplying catches most setup errors. For a unit rate, divide the quantity by the unit (60 mg ÷ 5 mL = 12 mg/mL).

Worked example

A vial contains 60 mg of medication in 5 mL. How many milliliters contain 84 mg?

  1. Set the proportion with mg on top: 60 mg / 5 mL = 84 mg / x mL.
  2. Cross-multiply: 60x = 5 × 84 = 420.
  3. Divide: x = 420 ÷ 60 = 7 mL.
  4. Check: 84 mg is 1.4 times 60 mg, and 5 × 1.4 = 7 mL, so the answer is reasonable.

Traps that cost marks

Moving the decimal one place instead of two when converting a percent. Using the new value as the base for a percent decrease (an $80 item marked down 25% costs $60, not $64). Placing matching units diagonally in a proportion. Rounding mid-calculation and then rounding again. Treating "percent of" and "percent more than" as the same operation.