Physics Lesson 1.1 The Metric System and Dimensional Analysis

Lesson 2.1 The Metric System and Dimensional Analysis I. The Metric System A The metric system is an internationally agreed decimal system of measurement that was originally based on the mètre des Archives and the kilogramme des Archives introduced by France in Over the years, the definitions of the meter and kilogram have been refined and the metric system has been extended to incorporate many more units. 2. Although a number of variants of the metric system emerged in the late nineteenth and early twentieth centuries, the term is now often used as a synonym for "SI"or the "International System of Units"—the official system of measurement in almost every country in the world.

Lesson 2.1 The Metric System and Dimensional Analysis B. Each unit within the metric system with a prefix is a division or multiple of the standard base unit value. 1. Prefixes correspond to specific divisions or multiples.

Lesson 2.1 The Metric System and Dimensional Analysis C. When making measurements in science, SI units (metric units) are the preferred unit of measurement. II. Dimensional Analysis A. The process of converting from one unit of measure to another for a given quantity. 1. Dimensional analysis involves the use of a conversion factor. 2. A conversion factor is a quantity stating the equivalence between two units of measure.

Lesson 2.1 The Metric System and Dimensional Analysis B. Metric unit to metric unit conversions. 1. Example: Convert 32.0 decameters into centimeters. a. Set up three fractions. i. Fraction 1 will contain the given quantity over 1. ii. Fraction 2 will contain the conversion factor that relates the given quantity to the base unit. iii. Fraction 3 will contain the conversion factor that relates the base unit to the desired quantity. Notice that all units will cancel except the desired unit. = cm Box your answer.

Lesson 2.1 The Metric System and Dimensional Analysis 2. Example: Convert 19.5 mL into daL. a. Set up three fractions. i. Fraction 1 will contain the given quantity over 1. ii. Fraction 2 will contain the conversion factor that relates the given quantity to the base unit. iii. Fraction 3 will contain the conversion factor that relates the base unit to the desired quantity. Notice that all units will cancel except the desired unit. = 1.95 x daL or Box your answer.

Lesson 2.1 The Metric System and Dimensional Analysis 3. Example: convert 4.18 kg into cg. a. Set up three fractions. i. Fraction 1 will contain the given quantity over 1. ii. Fraction 2 will contain the conversion factor that relates the given quantity to the base unit. iii. Fraction 3 will contain the conversion factor that relates the base unit to the desired quantity. Notice that all units will cancel except the desired unit. = 418,000 cg Box the answer

Lesson 2.1 The Metric System and Dimensional Analysis C. Dimensional Analysis between non-metric units. 1. The process is identical to that of metric conversion, but involves the use of different conversion factors. 2. Example: convert 3 dozen into a number of individual eggs. i. Set up 2 fractions. ii. Fraction 1 will contain the given quantity. iii. Fraction 2 will contain the conversion factor. = 36 eggs Box your answer

Lesson 2.1 The Metric System and Dimensional Analysis 3. Example: convert 3 days to seconds. In time conversions you may want to add fractions as conversion factors are needed. Notice that all units will cancel except the desired unit. = sec. Box your answer

Lesson 2.1 The Metric System and Dimensional Analysis 4. Example: convert 335 mg into pounds. This type of conversion requires additional conversion factors that relate non-metric units to metric units. The conversion factor here is pound = 1 kg. a. Set up four fractions. i. Fraction 1 will contain the given quantity over 1. ii. Fraction 2 will contain the conversion factor that relates the given quantity to the base unit. iii. Fraction 3 will contain the conversion factor that relates the base unit to the metric term related to the non-metric conversion factor. iv. Fraction 4 will include the metric term related to the non-metric conversion factor and the non-metric conversion factor. Notice that all units will cancel except the desired unit. = x pounds or pounds Box your answer