Lesson 6: Unit Conversions and Scientific Notation
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1 Lesson 6: Unit Conversions and Scientific Notation
2 Introduction: The metric system s many prefixes allow quantities to be expressed in many different units. Dimensional analysis is useful to convert from one metric system unit to another.
3 SI Prefixes: Prefix Abbreviation Exponential factor Meaning mega kilo Hecto Deca base deci centi milli M k H or h Da or D d c m ,000,000 1, / / /1000
4 SI Prefix examples: 1 kilometer = 1,000 meters 1 hectometer = 100 meters 1 decameter = 10 meters 1 decimeter = 0.1 meters ( one tenth of a meter ) 1 centimeter = 0.01 meters ( one hundredth of a meter ) 1 millimeter = meters ( one thousandth of a meter )
5 Scientific Notation: A mathematical expression used to represent a decimal number between 1 and 10 multiplied by ten, so you can write large numbers using less digits.
6 Scientific Notation: 1,000,000. How many times did we move the decimal? Is the original number GREATER THAN or LESS THAN zero?
7 Scientific Notation: What is in front of the decimal POSITIVE NUMBER because our original number was greater than zero! 1,000,000. = 1 x 10 6 Number of times we moved the decimal How many times did we move the decimal? Is the original number GREATER THAN or LESS THAN zero?
8 Scientific Notation: What is in front of the decimal NEGATIVE NUMBER because our original number was greater than zero! = 7.11 x 10-3 Number of times we moved the decimal How many times did we move the decimal? Is the original number GREATER THAN or LESS THAN zero?
9 Scientific Notation EXPONENT = number of decimal places that the decimal needs to be moved to change the number to standard notation 4.2 x 10 3 COEFFICIENT always between 1 and 10 BASE is 10
10 Scientific Notation 1. Coefficient is greater than or equal to 1 and less than Base is Exponent shows the number of decimal places that the decimal needs to be moved to change the number to standard notation. A negative exponent means that the decimal is moved to the left when changing to standard notation.
11 Scientific Notation Practice
12 Unit Conversions: Follow along to draw the formula for calculating unit conversions:
13 UNITS YOU END UP WITH unit multiplier = 1 1 WHAT YOU START WITH UNITS YOU START WITH ANSWER
14 Density Density is the amount of matter in a given volume Equation: Density = mass volume Multiply the values for mass by volume. Units are also divided, ending up as g/ml or g/cm 3 Often expressed in grams per cubic centimeter (g/cm 3 ) or grams per milliliter (g/ml) Density can be used to identify substances Substances may appear to be the same, yet they have different densities. Density does not change for a substance, no matter how big the sample is.
15 Archimedes Ancient Greek philosopher One of the earliest mathematicians Used density to solve a riddle of a king s crown
16 The Riddle of the King s Crown Did the goldsmith replace some of the gold given to him by an equal weight of silver? Hiero asked Archimedes to determine whether the wreath was pure gold. The wreath was a holy object - the could not disturb the wreath in any way.
17 The Riddle of the King s Crown SOLUTION = EUREKA! When he stepped into his bath and caused it to overflow. PLAN! Put a weight of gold equal to the crown, and known to be pure, into a bowl which was filled with water to the brim. Remove gold and king s crown put in. An alloy of lighter silver would increase the bulk of the crown and cause the bowl to overflow.
18 The Riddle of the King s Crown Relied on density = gold is more dense than silver Pure gold crown More dense Displaces less water Gold + Silver crown Less dense Displaces more water If the weight (mass) of each crown is the SAME, the imposter crown must have a larger volume to compensate.
19 Archimedes Principle Definition: the buoyant force experienced by a submerged object is equal to the weight of the water it displaces. Application: the volume of water displaced by an irregularly shaped solid that is not buoyant equals the volume of the solid.
20 Facts: The density of water is 1 g/ml. 1 ml = 1 cm 3 1 kg = 1000 g Therefore The mass of the water displaced is 2000 g. The volume of water displaced is 2000 ml. The volume of the metal object is 2000 cm 3
21
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