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## Units

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**Unit Systems**• Systems set up fundamental units. • British system - foot, pound, second • Metric system - meter, kilogram, second**Time**• The unit of time originally was based on the day and the year. • The second was 1/60 * 1/60 *1/24 of a day. • In the 20th century the second was measured based on the timing of atoms. • We now know that the day is getting longer and “leap seconds” are added every few years. • The SI unit of time is the second (s)**Length**• The oldest standards of length were based on the human body. • The metric system defined the meter in terms of the Earth: 1/10,000,000 from the pole to the equator. • The meter is now defined in terms of the second and speed of light. • The SI unit of length is the meter (m)**Mass**• Standard weights have been maintained for centuries. • Weight and mass were thought to be the same. • Now a standard 1 kilogram mass is kept in Paris. • The SI unit of mass is the kilogram (kg)**Prefixes on units are used to represent powers of ten.**Prefixes denote powers of ten from -18 to +18 in steps of three. Example: a kilometer is 103 meters or 1000 meters. Most Common micro () 10-6 milli (m) 10-3 kilo (k) 103 mega (M) 106 Common, but the power is not a factor of three. centi (c ) 10-2 deci (d ) 10-1 SI Prefixes**There are other fundamental units in SI. See NIST.**ampere (A) kelvin (K) mole (mol) candela (cd) Derived units are built from the fundamental units. area (m2) volume (m3) velocity (m/s) acceleration (m/s2) force (kg m/s2) or (N) energy (kg m2/s2) or (J) Other Units**Density**• Matter has mass and takes up volume. • The ratio of the mass to the volume is the density. Salt (solid): 2.165 x 103 kg/m3 Water (liquid): 1.000 x 103 kg/m3 Nitrogen (gas): 1.251 kg/m3**Matching Units**• Conversion between units must be of the same type. • Length conversion: • 1 in = 2.54 cm • Time conversion: • 1 hr = 3.6 x 103 s • No conversion between different types of units. • 1 in is not equivalent to some seconds**Conversion Factors**• A value is converted by applying the ratio of the conversion factors. • How many inches in 50. cm? • 50. cm (1 in / 2.54 cm) = (50. / 2.54) in = 20. in • Many conversion factors use scientific notation. • How many seconds in a year? • 1 yr (365 d/yr) (24 hr/d) (3.6 x 103 s/hr) = 31500 x 103 s = 3.15 x 107 s next