Question

How can I find the percentage change in mass from initial mass, final mass and mass difference in the calculation?

Answer 1

To find the percentage change in mass based on the initial mass and final mass, you can use the following formula:

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

If you have the mass difference instead of direct final and initial masses, you can express it as:

\[
\text{Mass Difference} = \text{Final Mass} - \text{Initial Mass}
\]

So you can rearrange the percentage change formula in terms of mass difference:

1. Substitute the mass difference into the percentage change formula:

\[
\text{Percentage Change} = \left( \frac{\text{Mass Difference}}{\text{Initial Mass}} \right) \times 100
\]

This allows you to calculate the percentage change using the mass difference directly. Here's a step-by-step breakdown:

1. **Calculate the Mass Difference:**
\[
\text{Mass Difference} = \text{Final Mass} - \text{Initial Mass}
\]

2. **Use the Mass Difference to Calculate Percentage Change:**
\[
\text{Percentage Change} = \left( \frac{\text{Mass Difference}}{\text{Initial Mass}} \right) \times 100
\]

### Example:
- **Initial Mass:** 200 g
- **Final Mass:** 180 g
- **Mass Difference:**
\[
180 \, \text{g} - 200 \, \text{g} = -20 \, \text{g}
\]
- **Percentage Change:**
\[
\left( \frac{-20 \, \text{g}}{200 \, \text{g}} \right) \times 100 = -10\%
\]

In this example, there was a 10% decrease in mass.