2.1 Measurement Systems Measurement is the determination of the dimensions, capacity, quantity, or extent of something. Copyright © Houghton Mifflin Company. All rights reserved.

2.1 Measurements in Chemistry always consists of two parts NUMBER EXACT or INEXACT SIGNIFICANT FIGURES SCIENTIFIC NOTATION UNIT METRIC SYSTEM DIMENSIONAL ANALYSIS Copyright © Houghton Mifflin Company. All rights reserved.

2.1 Metric System Units System Internationale (SI) Mass kilogram (kg), gram (g) Length meter (m), centimeter (cm) Volume cubic meter (m3), cubic centimeter (cm3) liter (L) = 1000 cm3 (exact) milliliter (mL) = 1 cm3 (exact) Time second (s) Temperature kelvin (k) Celsius (ºC) Copyright © Houghton Mifflin Company. All rights reserved.

Numerical prefixes for larger or smaller units: Common Metric System Prefixes with Their Symbols and Mathematical Meanings. Numerical prefixes for larger or smaller units: mega (M) 1000000 times unit (106) kilo (k) 1000 times unit (103) deci (d) 0.01 times unit (10-1) centi (c) 0.01 times unit (10-2) milli (m) 0.001 times unit (10-3) micro (µ) 0.000001 times unit (10-6) My King Died Chewing M & M’s Memorize these! Copyright © Houghton Mifflin Company. All rights reserved.

Figure 2. 2. Comparisons of the base metric system Figure 2.2 Comparisons of the base metric system units of length (meter), mass (gram), and volume (liter) with common objects. Copyright © Houghton Mifflin Company. All rights reserved.

Derived Units in the Metric System. Frequency (cycles/s, hertz) Density (mass/volume, g/cm3) Speed (distance/time, m/s) Acceleration (distance/(time)2, m/s2) Force (mass x acceleration, kg•m/s2, newton) Pressure (force/area, kg/(m•s2), pascal) Energy (force x distance, kg•m2/s2, joule) Copyright © Houghton Mifflin Company. All rights reserved.

2.3 Exact and Inexact Numbers Have no uncertainty associated with them From measurement of indivisible objects 10 tennis balls 29 students enrolled Some conversion factors Exactly 2.54 centimeters = one inch Copyright © Houghton Mifflin Company. All rights reserved.

2.3 Exact and Inexact Numbers Have some uncertainty associated with them From scalar measurements “Stuff” rather than “Things” Values are limited by the instrument 14.3 gallons ( 6 oz) 14.325 gallons ( 1 tsp) Copyright © Houghton Mifflin Company. All rights reserved.

2.4 Uncertainty in Measurement and Significant Figures Significant figures (sig figs or sig digs) are the digits in an inexact number. The last digit in an inexact number is an estimated value. The number of sig figs depends upon the instrument used. 14.3 gallons 14.325 gallons Copyright © Houghton Mifflin Company. All rights reserved.

2.4 Uncertainty in Measurement and Significant Figures Exact numbers have an infinite number of significant figures. They do not contain an estimated value. 10 tennis balls 2.54 cm = 1 inch Copyright © Houghton Mifflin Company. All rights reserved.

2.5 Significant Figures and Mathematical Operations When is zero a significant figure? Trailing zeros are always sig. figs. 11.0 ____ sig. figs. 100 ____ sig. figs. Trailing zeros are significant because they are the best estimate of the value. 10.9 11.0 (best estimate) 11.1 Copyright © Houghton Mifflin Company. All rights reserved.

2.5 Significant Figures and Mathematical Operations When is zero a significant figure? Embedded zeros are always sig. figs. 101 ____ sig. figs. 10.11 ____ sig. figs. Leading zeros are never sig. figs. 0.00145 ____ sig. figs. 0.0000000000234 ____ sig. figs. Copyright © Houghton Mifflin Company. All rights reserved.

Chemistry at a Glance: Significant Figures Copyright © Houghton Mifflin Company. All rights reserved.

2.5 Significant Figures and Mathematical Operations Multiplication and Division The result can have no more sig. figs. than the fewest number of sig. figs. used to obtain the result. 4.242 x 1.23 = 5.21766 5.22 12.24 / 2.0 = 6.12 6.1 Copyright © Houghton Mifflin Company. All rights reserved.

2.5 Significant Figures and Mathematical Operations Addition and Subtraction Result will have a digit as far to the right as all the numbers have a digit in common 2.02 8.7397 1.234 -2.123 + 3.6923 6.6167 6.9463 6.95 6.617 Copyright © Houghton Mifflin Company. All rights reserved.

2.5 Significant Figures and Mathematical Operations Rounding Off When the last sig. fig. is followed by a number equal to or greater than 5, round the last sig. fig. up. When the last sig. fig. is followed by a number less than 5, leave the last sig. fig. as is. Copyright © Houghton Mifflin Company. All rights reserved.

2.6 Scientific Notation Used for very large or very small numbers Distance from earth to sun 93,000,000 miles Diameter of a carbon atom 0.000000000015 meters Copyright © Houghton Mifflin Company. All rights reserved.

2.6 Scientific Notation An ordinary decimal number is expressed as the product of a coefficient between 1 and 10, and an exponential term. Express in scientific notation: 93,000,000 miles 0.000000000015 meters Copyright © Houghton Mifflin Company. All rights reserved.

2.6 Scientific Notation Scientific notation is useful for handling significant figures. Give the result to the proper number of significant figures: (25.456 – 25.423) x 64.58 x 430 = 0.01553  45.0 = Copyright © Houghton Mifflin Company. All rights reserved.

2.7 Conversion Factors and Dimensional Analysis A conversion factor is a ratio that specifies how one unit of measurement is related to another: 1 inch = 2.54 cm _1 in__ 2.54 cm 2.54 cm 1 in Copyright © Houghton Mifflin Company. All rights reserved.

2.7 Conversion Factors and Dimensional Analysis Dimensional analysis is a problem-solving method in which the units of the meas-urement are used to set up the calcula-tion. Units behave like numbers, they can be multiplied, divided, or cancelled. Copyright © Houghton Mifflin Company. All rights reserved.

2.7 Conversion Factors and Dimensional Analysis What is the volume of a cube if its edges are 2.5 cm long? How long is a foot in centimeters? Convert 0.0256 mm to m. Copyright © Houghton Mifflin Company. All rights reserved.

2.7 Conversion Factors and Dimensional Analysis How many miles will I travel in 3.00 hours at 65.0 miles per hour? How long will it take to travel 500 miles at 65 miles per hour? What is my speed, in miles per hour, if I ride my bike 25.5 miles in 1.20 hours? Copyright © Houghton Mifflin Company. All rights reserved.

2.8 Density Matter has mass and volume. Density is the ratio of mass to volume for a specific type of matter. Density = _mass_ _grams_ volume milliliters Density is a characteristic property of a pure substance. Copyright © Houghton Mifflin Company. All rights reserved.

Left: Shortening floats on water. Right: Copper floats on mercury Copyright © Houghton Mifflin Company. All rights reserved.

Liquids that do not dissolve in one another and that have different densities float on one another, forming layers. Copyright © Houghton Mifflin Company. All rights reserved.

Table 2.3 Densities of Selected Substances Copyright © Houghton Mifflin Company. All rights reserved.

2.8 Density Water has a density of 1.00 g/mL at 20°C. What is the mass of 20.0 mL of water? 20.0 mL of gasoline has a mass of 11.2 g. What is its density? What volume of ethyl alcohol will have a mass of 20.0 g? Its density is 0.79 g/mL. Copyright © Houghton Mifflin Company. All rights reserved.

2.9 Temperature Scale and Heat Energy Heat is a form of energy. Temperature can be used to measure heat. 1 calorie = amount of heat required to raise temperature of 1 gram of water by 1 Celcius 1 Calorie = 1000 calories = 1 kcal 1 Calorie = 4.184 Joule Copyright © Houghton Mifflin Company. All rights reserved.

The relationships among the Celsius, Kelvin, and Fahrenheit temperature scales are determined by the degree sizes and the reference point values. Copyright © Houghton Mifflin Company. All rights reserved.