A molecule is measured and the width is \( 3 \times 10^{-6} \mathrm{~cm} \). How long will a string of 22.5 similar molecules be? Give your answer in scientific notation.

To find the total length of a string of 22.5 similar molecules, we can follow these steps: 1. **Identify the width of one molecule**: The width of one molecule is given as \( 3 \times 10^{-6} \) cm. 2. **Calculate the total length of 22.5 molecules**: We multiply the width of one molecule by the number of molecules (22.5). \[ \text{Total Length} = \text{Width of one molecule} \times \text{Number of molecules} \] Substituting the known values: \[ \text{Total Length} = (3 \times 10^{-6} \, \text{cm}) \times 22.5 \] 3. **Perform the multiplication**: First, we multiply the coefficients: \[ 3 \times 22.5 = 67.5 \] Next, we keep the power of ten: \[ \text{Total Length} = 67.5 \times 10^{-6} \, \text{cm} \] 4. **Convert to scientific notation**: To express \( 67.5 \) in scientific notation, we can write it as \( 6.75 \times 10^1 \). Therefore, we have: \[ 67.5 \times 10^{-6} = 6.75 \times 10^1 \times 10^{-6} = 6.75 \times 10^{-5} \, \text{cm} \] Thus, the total length of a string of 22.5 similar molecules is \[ \boxed{6.75 \times 10^{-5}} \, \text{cm}. \]