Calculate Percentage Change Between Two Negative Numbers

What is Percentage Change?

Percentage change measures how much a quantity has increased or decreased relative to its original value. It's calculated by comparing the difference between the new and old values to the original value, then expressing that difference as a percentage.

For positive numbers, this is straightforward. However, when dealing with negative numbers, the interpretation changes slightly because the direction of change (increase or decrease) affects the sign of the percentage change.

Calculating Percentage Change with Negative Numbers

When both numbers are negative, the calculation follows the same formula as with positive numbers. The key is to remember that:

• If the new value is more negative (less than the original), it's a decrease
• If the new value is less negative (more than the original), it's an increase

The percentage change will be positive if the value becomes less negative (an increase) and negative if it becomes more negative (a decrease).

The Formula

For negative numbers, the calculation works the same way. The sign of the result indicates the direction of change:

• Positive result: The value has increased (become less negative)
• Negative result: The value has decreased (become more negative)

Worked Example

Let's calculate the percentage change between two negative numbers:

Original value: -50
New value: -40

Calculation:

The result is -20%, which means the value has decreased by 20% (it's now 20% more negative than the original value).

Common Mistakes

When working with negative numbers, these common errors can occur:

1. Forgetting to include the negative signs in calculations
2. Misinterpreting the sign of the percentage change
3. Confusing percentage change with absolute change