Perform each unit conversion. a. 28.9 nm to mm b. 1432 cm3 to L c. 1211 Tm to Gm

검증된 단계별 안내

Step 1: Identify the conversion factors needed for each unit conversion. For example, 1 nm = 1 x 10^{-9} m, 1 mm = 1 x 10^{-3} m, 1 cm^3 = 1 mL, 1 L = 1000 mL, 1 Tm = 1 x 10^{12} m, and 1 Gm = 1 x 10^9 m.

Step 2: For part a, convert 28.9 nm to mm by first converting nanometers to meters using the conversion factor 1 nm = 1 x 10^{-9} m, then convert meters to millimeters using 1 mm = 1 x 10^{-3} m.

Step 3: For part b, convert 1432 cm^3 to L by using the conversion factor 1 cm^3 = 1 mL, then convert milliliters to liters using 1 L = 1000 mL.

Step 4: For part c, convert 1211 Tm to Gm by first converting terameters to meters using 1 Tm = 1 x 10^{12} m, then convert meters to gigameters using 1 Gm = 1 x 10^9 m.

Step 5: Perform the calculations for each conversion using the identified conversion factors to find the final values in the desired units.

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주요 개념

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Unit Conversion

Unit conversion is the process of converting a quantity expressed in one set of units to another. This involves using conversion factors, which are ratios that express how many of one unit are equivalent to another. For example, to convert nanometers to millimeters, one would use the conversion factor that 1 mm equals 1,000,000 nm.

Metric System

The metric system is a decimal-based system of measurement used globally, which includes units such as meters, liters, and grams. It is organized in powers of ten, making it easier to convert between units by simply moving the decimal point. Understanding the prefixes (like nano-, centi-, and tera-) is essential for effective conversions within this system.

Volume and Length Conversions

Volume and length conversions require specific attention to the units involved, as they measure different dimensions. For instance, converting cubic centimeters (cm³) to liters (L) involves recognizing that 1 L equals 1,000 cm³. Similarly, converting terameters (Tm) to gigameters (Gm) requires understanding the relationship between these large units, where 1 Tm equals 1,000 Gm.