Finding Percent of Change

Concept

The percentage change (or) the percentage change of a quantity is the ratio of the difference in the quantity to its initial value multiplied by 100. There is always a change in percentage change (or) the percent change of a quantity when the percent of its initial value is either increased or decreased to obtain its final value.

Rules

Percent of Change:
Calculate the percent change using the equation

Percent change = $\fn_phv \frac{New\; Value \; - \; Old \; Value}{Old \; Value}$ × 100%

If the result is positive, it is an increase
If the result is negative, it is a decrease

Percent Error
Calculate the percent error using the equation

Percent error = $\fn_phv \frac{Amount\; of\; error}{Actual\; Amount}$ × 100%

Example

Find the percent of change.
50 meters to 40 meters

Solution

Percent change = $\fn_phv \frac{40m \; - \; 50m}{50m}$ × 100%

Percent change = $\fn_phv \frac{-10m}{50m}$ × 100%

Percent change = -0.2 x 100%
Percent change = -20%
Answer: 20% decrease

Practice Finding Percent of Change

Practice Problem 1

Find the percent of the increase. Round to the nearest whole percent if necessary.
27 liters to 32 liters.

Practice Problem 2

Find the percent of decrease. Round to the nearest whole percent if necessary.
89 seconds to 62 seconds.

Practice Problem 3

Find the percent of change and determine if it is an increase or decrease. Round to the nearest whole percent if necessary.
The minimum wage started at $6.55 in 2000 but was changed to $9.20 in 2015.

Practice Problem 4

Calculate the percent error. Round to the nearest whole percent.
Wesley guessed they would give out 55 free samples. They actually gave out 82.

Percentage Change is the difference coming after subtracting the old value from the new value and then divide by the old value and the final answer will be multiplied by 100 to show it as a percentage.

Pre-requisite Skills
Calculating Percent
Estimating Percent
Solving Percent Problems Using Proportions
Solving Percent Problems Using Equations