3. Decimals and Percent Reasoning

Decimals, fractions, and percents are three names for the same ratio.

Decimal to percent: multiply by 100 (move point two places right). \(0.048 \to 4.8\%\).

Percent to decimal: divide by 100 (move point two places left). \(135\% \to 1.35\).

Percent of a number: \(\text{part} = \text{rate} \times \text{whole}\). \(40\%\) of \(75 = 0.40 \times 75 = 30\).

Finding the whole: \(\text{whole} = \dfrac{\text{part}}{\text{rate}}\). If \(18\) is \(30\%\) of \(x\), then \(x = 18 \div 0.30 = 60\).

Percent change:
\[ \text{percent change} = \frac{\text{new} - \text{original}}{\text{original}} \times 100\%. \]
A price drops from \$50 to \$35: change is \(-15\), so percent change \(= -15/50 = -30\%\) (a 30% decrease).

Percent markup / markdown: markup adds to cost; tax adds to price. Combine by multiplying factors.
A \$120 item with 25% markup and 8% tax: \(120 \times 1.25 \times 1.08 = \$162\).