Percent Change and Error
Calculate percent increase and percent decrease using the formula (change ÷ original) × 100. Apply to population growth, price changes, and measurement error contexts.
A lesson of Pre-Algebra, in Ratios, Rates & Proportional Reasoning, about 10 minutes.
Percent Change
By the end of this lesson, you will be able to calculate percent increase and percent decrease and apply them to real-world contexts.
Percent Change Formula
$$\text{Percent Change} = \frac{\text{New} - \text{Old}}{\text{Old}} \times 100%$$
Positive result = percent increase; negative result = percent decrease.
Examples
Percent increase: Population grew from 5,000 to 6,500.
$\frac{6500 - 5000}{5000} \times 100 = \frac{1500}{5000} \times 100 = 30%$ increase
Percent decrease: Price dropped from $80 to $60.
$\frac{60 - 80}{80} \times 100 = \frac{-20}{80} \times 100 = -25%$ → 25% decrease
Finding the New Value
After a 15% increase from $200:
New = $200 \times 1.15 = $230$
After a 30% decrease from $50:
New = $50 \times 0.70 = $35$
Percent Error
$$\text{Percent Error} = \frac{|\text{Estimated} - \text{Actual}||}{\text{Actual}} \times 100%$$
Used to measure how far off an estimate is.
Example: Estimated 40 people; actual 45.
$\frac{|40-45|}{45} \times 100 = \frac{5}{45} \times 100 \approx 11.1%$ error
Summary
Percent change: $\frac{\text{New} - \text{Old}}{\text{Old}} \times 100%$; positive = increase, negative = decrease.
Finding new value: multiply old by $(1 + r)$ or $(1 - r)$.
Percent error: how far off an estimate is from the actual value.