Do Now: Calculate the following. a)(1.3 x 10 3 ) + (8.1 x 10 3 ) b)(9.4 x 10 6 ) – (5.3 x 10 6 ) c)(5.0 x 10 4 ) x (3.1 x 10 2 ) d)(6.3 x 10 9 ) (2.1 x 10 6 )
Do Now: Calculate the following. a)(1.3 x 10 3 ) + (8.1 x 10 3 ) = 9.4 x 10 3 b)(9.4 x 10 6 ) – (5.3 x 10 6 ) = 4.1 x 10 6 c)(2.0 x 10 4 ) x (3.1 x 10 2 ) = 6.2 x 10 6 d)(6.3 x 10 9 ) = 3.0 x 10 3 (2.1 x 10 6 )
YWBAT Explain what happens when a measurement is multiplied by a conversion factor Describe the kinds of problems that can be easily solved using dimensional analysis.
Quantities can usually be expressed in several different ways.
1 dollar = 4 quarters = 10 dimes 1 dollar= 20 nickels = 100 pennies
The same thing is true for scientific quantities. 1 meter = 10 decimeters = 100 centimeters 1 meter = 1000 millimeters These are all different ways to express the same length.
Conversion Factors A conversion factor is a ratio of equivalent measurements (aka – Funny Form of 1)
Conversion Factors When a measurement is multiplied by a conversion factor, the numerical value is usually changed but the actual size of the quantity measured remains the same.
Unit Prefixes
Conversion Factors What conversion factor would you use if you wanted to convert 9 teaspoons to tablespoons?
Conversion Factors What conversion factor would you use if you wanted to convert 9 teaspoons to tablespoons? 1 tablespoon = 3 teaspoons Conversion factor = 1 tablespoon 3 teaspoons 9 teaspoons x 1 tablespoon = 3 tablespoons 3 teaspoons
Conversion Factors What about significant figures? Remember – Conversion factors are defined or exact quantities. They have an unlimited number of significant figures and do not affect the rounding of a calculated answer.
Dimensional Analysis Dimensional Analysis is a way to analyze and solve problems using the units, or dimensions, of the measurements.
Dimensional Analysis If the exchange rate between U.S. dollars and euros is euro to every dollar, what is the conversion factor that allows you to convert from U.S. dollars to euros?
Dimensional Analysis If the exchange rate between U.S. dollars and euros is euro to every dollar, what is the conversion factor that allows you to convert from U.S. dollars to euros? The conversion factor to convert from U.S. dollars to euros would be Euro 1 US Dollar
Dimensional Analysis A complex problem may need more than one step. When converting between units, it is often necessary to use more than one converison factor.
Dimensional Analysis The diameter of a sewing needle is cm. What is the diameter in micrometers?
Dimensional Analysis The diameter of a sewing needle is cm. What is the diameter in micrometers?
Dimensional Analysis The diameter of a sewing needle is cm. What is the diameter in micrometers?
Dimensional Analysis The directions for an experiment ask each student to measure 1.84 g of copper (Cu) wire. The only copper wire available is a spool with a mass of 50.0 g. How many students can do the experiment before the copper runs out?
Dimensional Analysis The directions for an experiment ask each student to measure 1.84 g of copper (Cu) wire. The only copper wire available is a spool with a mass of 50.0 g. How many students can do the experiment before the copper runs out?