PharmD Summer Academy 2026: Decimals, Fractions & Exponents Flashcards

Vocabulary and rules for decimal operations, fraction manipulation, and exponent laws essential for PharmD calculation foundations.

Medication Error Risks

A single misplaced decimal point can shift a dose by a factor of 10 or 100.

Tenths Place

The first digit to the right of the decimal point, representing a value of $\frac{1}{10}$.

Hundredths Place

The second digit to the right of the decimal point, representing a value of $\frac{1}{100}$.

Thousandths Place

The third digit to the right of the decimal point, representing a value of $\frac{1}{1000}$.

Rule for Adding and Subtracting Decimals

Stack the numbers to line up every decimal point in the same column, adding zeros as placeholders if needed.

Rule for Multiplying Decimals

Multiply as whole numbers, count the total decimal places in both original numbers, and place the decimal point that many spots from the right.

Rule for Dividing Decimals

Move the decimal point in the divisor until it is a whole number, then move the decimal in the dividend the same number of places before dividing.

Numerator

The top part of a fraction indicating how many equal parts you have.

Denominator

The bottom part of a fraction indicating how many equal parts make the whole.

Simplifying Fractions

Divide the numerator and denominator by their greatest common factor (GCF) until the fraction is in its lowest terms.

Rule for Adding and Subtracting Fractions

Find a common denominator, convert each fraction, add or subtract the numerators, keep the denominator the same, and simplify.

Rule for Multiplying Fractions

Multiply straight across: numerator $\times$ numerator and denominator $\times$ denominator.

Keep, Change, Flip

The rule for dividing fractions: keep the first fraction, change $\div$ to $\times$, and flip (reciprocate) the second fraction.

$$\frac{1}{2}$$

$$0.5$$

$$\frac{1}{4}$$

$$0.25$$

$$\frac{3}{4}$$

$$0.75$$

$$\frac{1}{3}$$

$$0.333$$

$$\frac{2}{3}$$

$$0.667$$

$$\frac{1}{8}$$

$$0.125$$

$$\frac{1}{5}$$

$$0.2$$

$$\frac{1}{10}$$

$$0.1$$

Base

The number in an exponent expression that is being multiplied by itself.

Exponent

The number that indicates how many times the base multiplies itself.

Product Rule

$a^m \times a^n = a^{m+n}$; when multiplying the same base, add the exponents.

Quotient Rule

$a^m \div a^n = a^{m-n}$; when dividing the same base, subtract the exponents.

Power Rule

$(a^m)^n = a^{m \times n}$; when taking a power of a power, multiply the exponents.

Zero Exponent Rule

Any nonzero number raised to the power of 0 equals 1 ($a^0 = 1$).

Negative Exponent Rule

A negative exponent means taking the reciprocal: $a^{-n} = \frac{1}{a^n}$.

Scientific Notation (Small Numbers)

Move the decimal right until one nonzero digit remains to the left; the number of moves is expressed as a negative power of 10.

Scientific Notation (Large Numbers)

Move the decimal left until one nonzero digit remains; the number of moves is expressed as a positive power of 10.