TEAS® Math Study Guide
Percentages & Conversions
A percent means "per hundred." It is the representation of a number as a fraction out of 100. Thus, 50\% literally means 50 out of 100, or:
\(50\% = \dfrac{50}{100} = 0.5\)
You can convert between percent, fraction, and decimal forms.
To convert a decimal to a percent, multiply by 100 (move the decimal two places to the right).
Example: Convert 0.2 to a percent:
\(0.2 = 0.2 \times 100\% = 20\%\)
To convert a percent to a decimal, divide by 100 (move the decimal two places to the left).
Example: Convert \(33\%\) to decimal.
\(33\% = \dfrac{33}{100} = 0.33\)
To convert a fraction to a percent, convert it first to a decimal by dividing the numerator by the denominator and then multiply by 100.
Example: Convert \(\dfrac{3}{5}\) to percent
\(\dfrac{3}{5} = 0.6 = 0.6 \times 100\% = 60\%\)
To convert a percent to a fraction, make the percent the numerator and 100 the denominator. Simplify the fraction that results.
Example: Convert 40% to a fraction.
\(40\% = \dfrac{40}{100} = \dfrac{2}{5}\)
| Start With | Convert to Decimal | Convert to Percent |
| Fraction | Divide numerator by denominator | Then multiply by 100 |
| Decimal | — | Multiply by 100 |
| Percent | Divide by 100 | — |
Tip: Use benchmarks to estimate quickly:
\(\dfrac{1}{2} = 50\%, \dfrac{1}{4} = 25\%,\)\(\dfrac{3}{4} = 75\%, \dfrac{1}{5}= 20\%\)
Percentage Calculation
To find a percentage of a quantity, multiply the number by the decimal form of the percent.
\(\text{Percentage of a number}\)\(= \text{Percent (as decimal)} \times \text{Quantity}\)
Example: \(30\%\) of \( 80 = 0.3 \times 80 = 24\)
Example: A nurse administers 12.5% of a 400 mL solution. How much solution was administered?
\(12.5\%\) of \(400 \ \text{mL} = 0.125 \times 400 = 50 \ \text{mL}\)
If the change percentage is positive, there has been an increase in quantity. If it is negative, there has been a decrease in quantity.
Example: A price goes from $80 to $100. What is the percentage change?
\(\text{Percentage Change} = \)\(\dfrac{\text{Final value – Initial value}}{\text{Initial value}} \times 100\)
\(\text{Percentage Change} = \)
\(\dfrac{100-80}{80} \times 100\)
\(\text{Percentage Change} = \)
\(\dfrac{20}{80} \times 100\)
\(\text{Percentage Change} =\)
\(25\%\)
Example: A medicine’s dosage is reduced from 200 mg to 150 mg. What is the percentage change?
\(\text{Percentage Change} = \)\(\dfrac{\text{Final value – Initial value}}{{\text{Initial value}}} \times 100\)
\(\text{Percentage Change} = \)
\(\dfrac{150-200}{200} \times 100\)
\(\text{Percentage Change} = \)
\(\dfrac{-50}{200} \times 100\)
\(\text{Percentage Change} = \)
\(−25\%\)
Tip: Always subtract final – initial, but divide by the initial amount.