Convert the following measurement. \[ 9.1 \times 10^{2} \frac{\mathrm{~kg}}{\mathrm{~m}^{3}}=\square \frac{\mathrm{g}}{\mathrm{cm}^{3}} \]

Calculate the value by following steps: - step0: Calculate: \(\frac{9.1\times 10^{2}\left(\frac{1000}{1}\right)}{100^{3}}\) - step1: Divide the terms: \(\frac{9.1\times 10^{2}\times 1000}{100^{3}}\) - step2: Multiply: \(\frac{9.1\times 10^{5}}{100^{3}}\) - step3: Factor the expression: \(\frac{9.1\times 10^{5}}{10^{6}}\) - step4: Reduce the fraction: \(\frac{9.1}{10}\) - step5: Convert the expressions: \(\frac{\frac{91}{10}}{10}\) - step6: Multiply by the reciprocal: \(\frac{91}{10}\times \frac{1}{10}\) - step7: Multiply the fractions: \(\frac{91}{10\times 10}\) - step8: Multiply: \(\frac{91}{100}\) To convert the measurement \( 9.1 \times 10^{2} \frac{\mathrm{~kg}}{\mathrm{~m}^{3}} \) to \( \frac{\mathrm{g}}{\mathrm{cm}^{3}} \), we can follow these steps: 1. **Understand the conversion factors**: - \( 1 \, \mathrm{kg} = 1000 \, \mathrm{g} \) - \( 1 \, \mathrm{m}^{3} = 100^3 \, \mathrm{cm}^{3} = 1,000,000 \, \mathrm{cm}^{3} \) 2. **Set up the conversion**: \[ 9.1 \times 10^{2} \frac{\mathrm{kg}}{\mathrm{m}^{3}} = 9.1 \times 10^{2} \frac{1000 \, \mathrm{g}}{1 \, \mathrm{kg}} \cdot \frac{1 \, \mathrm{m}^{3}}{1,000,000 \, \mathrm{cm}^{3}} \] 3. **Calculate the conversion**: \[ = 9.1 \times 10^{2} \cdot \frac{1000}{1,000,000} \, \frac{\mathrm{g}}{\mathrm{cm}^{3}} = 9.1 \times 10^{2} \cdot \frac{1}{1000} \, \frac{\mathrm{g}}{\mathrm{cm}^{3}} = 9.1 \times 10^{-1} \, \frac{\mathrm{g}}{\mathrm{cm}^{3}} \] 4. **Final result**: \[ 9.1 \times 10^{-1} \, \frac{\mathrm{g}}{\mathrm{cm}^{3}} = 0.91 \, \frac{\mathrm{g}}{\mathrm{cm}^{3}} \] Thus, the converted measurement is: \[ 0.91 \, \frac{\mathrm{g}}{\mathrm{cm}^{3}} \]