To find the change in height, we need to subtract the final height from the initial height.
- Initial height: \( \frac{1}{20} \) meter
- Final height: \( \frac{1}{50} \) meter
Now, we can calculate the change in height:
\[ \text{Change in height} = \text{Initial height} - \text{Final height} = \frac{1}{20} - \frac{1}{50} \]
To subtract these fractions, we need a common denominator. The least common multiple of 20 and 50 is 100. We can convert both fractions:
\[ \frac{1}{20} = \frac{5}{100} \quad (\text{Multiply both numerator and denominator by 5}) \] \[ \frac{1}{50} = \frac{2}{100} \quad (\text{Multiply both numerator and denominator by 2}) \]
Now we can perform the subtraction:
\[ \text{Change in height} = \frac{5}{100} - \frac{2}{100} = \frac{3}{100} \]
Thus, the change in height is
\[ \frac{3}{100} \text{ meter.} \]
So the correct answer is \( \frac{3}{100} \) meter.