414 CHAPTER 7 The Metric System Metric System Conversions Example 1 Converting from Basic Metric Units a) Convert 457.3 m to km. b) Convert 14 g to cg. c) Convert 0.53 to m . d) Convert 2450 to k . Solution a) Table 7.2 above shows that kilometers are larger units of measurement than meters. Kilometers appear three places to the left of meters in the table. Therefore, to change a measure from meters to kilometers, we must move the decimal point in the given number three places to the left, or 457.3 m 0.4573 km = Note that since we are changing from a smaller unit of measurement (meter) to a larger unit of measurement (kilometer), the answer will be a smaller number of units. b) Grams are a larger unit of measurement than centigrams. To convert grams to centigrams, we move the decimal point two places to the right, or 14 g 1400 cg = Note that since we are changing from a larger unit of measurement (gram) to a smaller unit of measurement (centigram), the answer will be a larger number of units. c) 0.53 530 m = d) 2450 2.45 k = 7 Now try Exercise 27 Did You Know? The Seven Base Units There are seven base units in the metric system. The definition of each of these base units is very technical. The seven base units are meter (for length), kilogram (for mass), second (for time), Kelvin (for temperature), ampere (for electrical current), candela (for illumination intensity), and mole (for material quantity). The technical definition of each of these base units can be found on many websites, including the U.S. National Institute of Standards, NIST.gov. There are many other metric units of measurement that are derived using these seven base units. For example, degrees Celsius , which is the primary temperature unit used in the metric system, is derived by subtracting 273.15 from the Kelvin temperature. A few of the many metric units derived from the seven base units that you may recognize include watt, hertz, volt, ohm, lumen, and radian. Example 2 Converting Metric Units a) Convert 704 mm to hectometers. b) Convert 6.34 dam to decimeters. c) Convert 0.004 561 kg to centigrams. d) Convert 1 345 000 mg to kilograms. Solution a) Table 7.2 shows that hectometers are five places to the left of millimeters. Therefore, to make the conversion, we must move the decimal point in the given number five places to the left, or 704 mm 0.007 04 hm = b) Table 7.2 shows that decimeters are two places to the right of dekameters. Therefore, to make the conversion, we must move the decimal point in the given number two places to the right, or 6.34 dam 634 dm = c) 0.004 561 kg 456.1 cg. = d) 1 345 000 mg 1.345 kg. = 7 Now try Exercise 41
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