(5) \( \begin{array}{l}\text { solve the metric measurement equation. } \\ 75.24 \mathrm{cg}-3 \mathrm{dg}=\square \mathrm{dg}\end{array} \)

To solve the equation: \[ 75.24\,\text{cg} - 3\,\text{dg} = \square\,\text{dg} \] we need to convert all measurements to the same unit. Let's convert everything to **decigrams (dg)**. ### Understanding Metric Prefixes: - **Centigram (cg)**: \(1\,\text{cg} = 0.01\,\text{g}\) - **Decigram (dg)**: \(1\,\text{dg} = 0.1\,\text{g}\) From this, we can deduce: - \(1\,\text{dg} = 10\,\text{cg}\) - Therefore, \(1\,\text{cg} = 0.1\,\text{dg}\) ### Conversion Steps: 1. **Convert 75.24 cg to dg:** \[ 75.24\,\text{cg} \times 0.1\,\frac{\text{dg}}{\text{cg}} = 7.524\,\text{dg} \] 2. **Subtract 3 dg:** \[ 7.524\,\text{dg} - 3\,\text{dg} = 4.524\,\text{dg} \] ### Final Answer: \[ 75.24\,\text{cg} - 3\,\text{dg} = 4.524\,\text{dg} \] **Rounded (if necessary):** \[ 4.524\,\text{dg} \approx 4.52\,\text{dg} \]