When there is a change in the values of some quantity, then we need to know the change value. Also sometimes it becomes more important to determine the percent change in the values. Students can compute it with the help of a simple formula. Sometimes to know the discounts change in price value or the change in prices of products or income, the percentage change formula proves much important. We express it in terms of percentage and it is the change in new value with respect to the old value. Further, the change in value is divided by the original value and then multiplied by 100. In this topic, we will discuss the percent change formula with examples. Let us learn it!

**Percent Change Formula**

**What Is Percent Change?**

The percentage error value is also very important under the experimental calculations. This formula is the absolute value of the difference of both values i.e. measured value and the theoretical value. Further, this change is divided by the theoretical value. Next, multiply it by 100. Percentage change is a simple but important mathematical concept that represents the degree of change over time. It is used for many areas like finance, often to represent the price change of security.

**Understanding the Concept:**

Percentage change can be applied to any quantity or term that we measure. Let us say we are tracking the quoted price of some security. If the price increased, then use the value as (New Price – Old Price). If the price decreased, then use the value as (Old Price – New Price). This formula is used to track the prices of individual securities as well as the large market indexes. Also, it can be used for comparing the values of different currencies.

**Percentage Change Formula:**

\(Percent Change = \frac{(Old Value –New Value)} {Old Value}\times 100\)

**Steps to Calculate: **

The simple step by step procedure is as below:

1. First, calculate the change (subtract old value from the new value)

2. Then divide that change by the old value (we may get a decimal number)

3. Finally, convert that to a percentage (by multiplying by 100 and adding a “%” sign)

Here, it must be noted that the change value must be positive. Thus when the new value is greater than the old value, then it is a percentage increase, otherwise, it is a decrease.

**Solved examples for Percent Change Formula**

Q.1: A selling price for a pair of socks change from ₹75 to ₹90. Calculate the percentage change in the selling price.

Solution:

Step 1: Calculate the change i.e. New value- old value

= 90-75 =15

Step 2: Divide that change value by the old value,

\(= \frac{ 15} {75} =\frac{1} {5}\)

Step 3: Convert that change to a percentage change value,

\(= \frac {1} {5} \times 100\)

= 20 %

Hence the percentage change in the selling price will be 20%.

Q.2: What will be the percentage change in the weight of Ram, if he reduces his weight to 77 kg from 82 kg?

Solution: Old weight = 82 Kg and New Weight = 77 Kg

Change in weight = Old value – New value

= 82 -77 = 5

Using the formula as below:

\(Percent Change = \frac{(Old Value –New Value)} {Old Value}\times 100\)

=\( \frac{ 5} { 82 } \times 100\)

= 6.4 %

Hence the percent change in his weight will be 6.4%

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