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Perform each unit conversion using dimensional analysis. Go through the base unit for each one.

a. Convert 27.8 L to cm³.

b. Convert 1898 mg to kg.

c. Convert 198 km to cm.

Answer :

Final answer:

In dimensional analysis, liters are converted to cubic centimeters using a conversion ratio of 1L = 1000 cm³, milligrams to kilograms utilizing the ratio 1 kg = 1,000,000 mg, and kilometers to centimeters with the conversion of 1 km = 100,000 cm. Consequently, 27.8 L is 27,800 cm³, 1898 mg equals 0.001898 kg, and 198 km comes to 19,800,000 cm.

Explanation:

To perform all the unit conversions and go through the base unit for each one using dimensional analysis, we start with transforming liters (L) to cubic centimeters (cm³). The conversion factor is 1 L = 1000 cm³, based on the base unit conversion. Hence, 27.8 L is equivalent to 27,800 cm³. We can express this as (27.8 L)*(1000 cm³ / 1 L) = 27,800 cm³.

Next, we convert milligrams (mg) to kilograms (kg) with 1kg = 1,000,000 mg. So, 1898 mg equals 0.001898 kg, which can be demonstrated as (1898 mg)*(1 kg / 1,000,000 mg) = 0.001898 kg.

Finally, we turn kilometers (km) to centimeters (cm). The conversion ratio is 1 km = 100,000 cm. Therefore, the conversion of 198 km to cm translates to 19,800,000 cm, shown by (198 km)*(100,000 cm / 1 km) = 19,800,000 cm.

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