Mathematical Formula For Calculating Percentage Change
\[ \text{Percentage Change} = \frac{\text{Final Value} – \text{Initial Value}}{\text{Initial Value}} \times 100 \]
Example Broken Down With Steps
$$
\text{Given: Initial Value = 100, New Value = 120}
$$
$$
\text{Step 1: Subtract 100 from 120: } 120 – 100 = 20
$$
$$
\text{Step 2: Divide 20 by 100: } \frac{20}{100} = 0.2
$$
$$
\text{Step 3: Multiply 0.2 by 100: } 0.2 \times 100 = 20
$$
$$
\text{Result: Percentage increased by 20%.}
$$
Further Explained
Example: A price increased from 100 to 120.
Steps:
- Find the absolute change: Subtract the original value from the new value to find how much it changed:
$$ 120 – 100 = 20 $$ - Divide the change by the original value: To find how large the change is compared to the original value:
$$ \frac{20}{100} = 0.2 $$ - Convert to a percentage: Multiply the result by 100 to express it as a percentage:
$$ 0.2 \times 100 = 20\% $$ - Conclusion: The percentage change is 20%.