Percent means “per hundred.” This chapter connects percent, fraction, and decimal forms and applies them in everyday contexts.

Percent, fraction, decimal

\(35\% = \frac{35}{100}=0.35\)

Convert by multiplying or dividing by 100 as needed.

Finding part and whole

To find \(p\%\) of a quantity \(Q\), use \(\frac{p}{100}\times Q\).

\(18\%\text{ of }250 = 0.18\times250 = 45\)

Percent increase and decrease

Percent change compares new and original values.

\[ \%\text{ change}=\frac{\text{new}-\text{original}}{\text{original}}\times 100\%. \]

New values can also be found with multipliers:

• Increase by \(r\%\): multiply by \(1+\frac{r}{100}\).
• Decrease by \(r\%\): multiply by \(1-\frac{r}{100}\).

Real-world applications

Discounts, tax, markups, interest, and error rates are all percentage models.

Checkpoint: 25% off a \$80 item

Discount \(=0.25\times80=20\), so sale price is \$60.

Checkpoint: increase 200 by 12%

\(200\times1.12=224\).