Percentage Change

Percentage change shows how much a value has increased or decreased from its original value and is expressed as a 100. There are two types of percentage change: percentage increase, when the final value is greater than the initial value, and percentage decrease, when the final value is less than the initial value. To calculate the percentage change, first divide the difference between the final and initial values by the initial value, then multiply by 1

\( \text{Percentage Change} = \left( \frac{\text{Final Value} - \text{Initial Value}}{\text{Initial Value}} \right) \times 100 \)

The percentage change formula is used to calculate the change in a value from its original value. It compares the change in value with the initial value and expresses the result as a percentage.

 \({\text {Percentage Change}} = {{{{\text {Change in Value} \over {\text {Initial Value}} }}{{\times 100}}}} \)
 

Percentage Increase Formula: The percentage increase is used when the final value is greater than the initial value. It is calculated using the formula:

\( \text{Percentage Change} = \left( \frac{\text{Final Value } - \text{ Initial Value}} {\text{Initial Value}} \right) \times 100 \)
 

Percentage Decrease Formula: The percentage decrease is used when the final value is less than the initial value. It is calculated using the formula: 
\(\text{Percentage Decrease} = \left( \frac{\text{Initial Value } - \text{ Final Value}} {\text{Initial Value}} \right) \times 100 \)

To compare the difference between the initial and final values, we use the percentage change. In this section, we will learn how to calculate percentage change with an example.

• Find the change by subtracting the initial value from the final value. 
   
• Divide the change by the initial value. 
   
• Multiply the value in step 2 by 100 and add the percentage sign (%).

For example, the price of a book increased from $200 to $250. Find the percent change. 

Step 1: Find the change 
Here, the final value is $250
The initial value is $200
So, the change \(= 250 - 200\)
= 50

Step 2: Dividing the change by the initial value 
Change = 50
Initial value = 200
So, \(50 ÷ 200 = 0.25\)

Step 3: Converting to a percentage 
0.25 × 100 = 25%

So, the percentage change is 25%.
  

Percentage change becomes easier to understand with a few simple tips. In this section, we will learn some tips and tricks to master percentage change.
 

• Memorize the basic formula for calculating percentage change, so students can apply it quickly and confidently. The formula is \( \text{Percentage Change} = \left( \frac{\text{Final Value } - \text{ Initial Value}} {\text{Initial Value}} \right) \times 100. \)
   

• Always identify the initial and final values correctly, as percentage change is always based on the initial value.
   

• Parents can use everyday situations to teach percentage change by talking about discounts while shopping and by identifying percentage increases and decreases. 
   

• Teachers can use visual and bar models to represent initial or final values. So that students can understand percentage change more quickly. 
   

• Always check the sign of the change to understand whether it is a percentage increase or decrease. If the difference is positive, it is a percentage increase; if negative, a percentage decrease.

Percentage change is used to compare how the value increases or decreases over time. It helps to understand changes in prices, salaries, bills, marks, and many other applications. Here are some applications of percentage changes. 

• When shopping, we calculate discounts using percentage change to show customers how much they are saving on the original purchase price. For example, if a $100 shirt is on sale for $80, the percentage decrease is 20%. 
   
• To calculate the salary increment, employees check their increment to see how much their salary has increased; for example, if employee A’s salary increased from $40,000 to $44,000, then the percentage increase = \({44,000 - 40,000 \over 40,000 }× 100 = 10\%\).
   
• In the stock market, investors use percentage change to assess the rise or fall in share prices when making decisions. For example, if the share of company A moved from $950 to $1045. Percentage change \(={ 1045 - 950 \over 950} × 100 = 10\%\).
   
• In finance, percentage change is used to calculate interest rates, profit margins, ROI, depreciation, taxes, and other financial ratios. For example, if an item costs $200 to produce and sells for $260, the profit percentage is \({60 \over 200} × 100 = 30\%\).
   
• Percentage change is used to track sales performance, plan marketing strategies, and analyze customer behavior. For example, if a company sells $2 million in product out of a $20 million market, its market share is 10%.