Notes. In order to make numbers more "friendly" looking, the metric system sometimes uses prefixes in the front of the base units.

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1 The Metric System By the eighteenth century, dozens of different units of measurement were commonly used throughout the world. Length, for example, could be measured in feet, inches, miles, spans, cubits, hands, furlongs, palms, rods, chains, leagues, and more. The lack of common standards led to a lot of confusion. At the end of the century, the French government sought to alleviate this problem by devising a system of measurement that could be used throughout the world. In 1795, the French National Assembly commissioned the Academy of Science to design a simple decimal-based system of units; the system they devised is known as the metric system. In 1960, the metric system was officially named the Système International d'unités (or SI for short) and is now used in nearly every country in the world except the United States. The metric system is almost always used in scientific measurement. The simplicity of the metric system stems from the fact that there is only one unit of measurement (or base unit) for each type of quantity measured (length, mass, etc.). Prefixes and Converting Units In order to make numbers more "friendly" looking, the metric system sometimes uses prefixes in the front of the base units. The metric system is called a decimal-based system because it is based on multiples of ten. Any measurement given in one metric unit (e.g., kilometer) can be converted to another metric unit (e.g., meter) simply by moving the decimal place.

2 The metric units for all quantities use the same prefixes. One thousandth of a gram is a milligram and one thousand grams is a kilogram. One thousandth of a second is a millisecond and one thousand seconds is a kilosecond. A ratio of values equal to one is called a conversion factor. Because the metric system is based on multiples of ten, converting within the system is quite simple. Conversion Factor

3 Scientific Notation In science, it is common to work with very large and very small numbers. Examples The diameter of a red blood cell is cm. The distance from the earth to the sun is 150,000,000 km. The number of molecules in 1 g of water is 3,400,000,000,000,000,000,000. Scientific notation is simply a method for expressing, and working with, very large or very small numbers. It is a short hand method for writing numbers. Numbers in scientific notation are made up of three parts: the coefficient, the base and the exponent. Example 5.67 x 10 5 exponent coefficient base This is the scientific notation for the standard number There are three rules for using scientific notation: Rule 1 To express a number in scientific notation, you move the decimal point to the position such that there is one nonzero digit to the left of the decimal point. Rule 2 If the decimal point is moved to the left, the exponent is positive. Rule 3 If the decimal point is moved to the right, the exponent is negative.

4 A mnemonic that may help you remember how to keep the signs straight is: Ruby Newton Loves Physics R N right --- negative L P left --- positive Examples 1. Express in scientific notation. Solution: = x 10-4 The decimal point was moved to the right four spaces. If the decimal point moves to the right, the exponent is negative. Since it moved four spaces, the exponent is a 4. Notice that the decimal point was moved until one and only one nonzero digit was in front of the decimal point. 2. Express 568 in scientific notation. Solution: 568 = 5.68 x 10 2 The decimal point was moved to the left two spaces. If the decimal point moves to the left, the exponent is positive. Since it moved two spaces, the exponent is a +2. Notice that the decimal point was moved until one and only one nonzero digit was in front of the decimal point.

5 Significant Figures Scientists take the ideas of precision and accuracy very seriously. We need to know that when a scientist reports a finding, we can trust the accuracy and precision of all their measurements. When determining the number of significant figures in a measurement, begin at the left and move to the right until you find the first non-zero digit. Count the first non-zero digit and every digit to the right of it significant figures first non-zero digit Examples 3 sig figs 4 sig figs 5 sig figs 25.0 m/s m/s m/s 2.50 m/s m/s m/s ml ml ml ml ml ml ml ml ml 8.07 x 10 6 m/s x 10 6 m/s x 10 6 m/s Zeroes used solely to fix the decimal point are not significant. To determine whether a zero is used as a place holder, write the number without the zero; if the number changes, (like 250 to 25 or to 17), the zero is not significant. All exact values or conversion factors have an infinite (never ending) number of significant figures. They are called exact values because they are measured in complete units and are not divided into smaller parts. You might count 8 people or 9 people but it is not possible to count 8.5 people. Examples of exact values: 12 complete waves ; 17 people ; 28 nails Examples of exact conversion factors: 60 s/minute ; 1000 m/km ; 12 eggs/dozen

6 There are exactly: 6o seconds in one minute 1000 meters in one kilometer [this is the definition of kilo (k)] 12 eggs in one dozen 7 days in one week Calculations When adding or subtracting the number of significant figures in your final answer is set by the value with the smallest number of decimal places. When multiplying or dividing the number of significant figures in your final answer is set by the value with the fewest significant figures.