Chapter 2 Data Analysis

Units of Measurement SI (Systém Internationale) Units are the units of science Base Units Time: Second Length: Meter Mass: Kilogram Derived Units: Units that are described by a combination of base units Volume: Liter Density: g/cm 3 or g/mL Temperature: Kelvin (C + 273)

Problem Solver What is the density of a cube whose sides are each 5 m and that measures 4.0 grams on the triple beam balance? What is the volume of a cube whose density is 25 g/cm 3 and mass is 5g? A thermometer displays a temperature of 28 o Celsius. What is its measurement in Kelvin?

Problem Solver Answers What is the density of a cube whose sides are each 5 cm and that measures 4.0 grams on the triple beam balance? 5 * 5 * 5 = 125 cm 3 4 g / 125 cm 3 = g/cm 3 What is the volume of a cube whose density is 25 g/cm 3 and mass is 5g? d = m/v 25 g/cm 3 = 5g/v 25v = 5 v = 5/25 = 0.2 cm 3 A thermometer displays a temperature of 28 o Celsius. What is its measurement in Kelvin? K = C K = K = 301

Scientific Notation Expresses numbers as a multiple of two (2) factors. Factor 1: A number between 1 and 10 raised to an exponent Factor 2: The exponent, which tells how many times factor 1 must be multiplied by 10. Example x x Layout Factor 1 x 10 Factor 2

Scientific Notation, Continued Adding and Subtracting 1.Make sure all numbers are in proper scientific notation 2.Make sure the exponents are the same 3.Add/Subtract the numbers DO NOT add/subtract the 10 n 4.You will end-up with a number in scientific notation

Scientific Notation, Continued Multiplying and Dividing 1.Make sure all numbers are in proper scientific notation 2.For Multiplications, Multiply Factor 1. For division, divide Factor 1. 3.For Multiplication, ADD the exponents. For division, subtract the exponents. 4.You will end-up with a number in scientific notation

In-Class Practice Page 32 Practice Problems 12 a 12 c 12 e 12 g 14 a 14 b 14 d 14 f Page 33 Practice Problems 15 a 15 b 15 c 15 d 16 a 16 b 16 c 16 d

Dimensional Analysis Moving from one unit type to another unit type Conversion Factor: A ratio of equivalent values used to express the same quantity in different units. A conversion factor is ALWAYS equal to one Change the unit of quantity without changing the values Meters to Kilometers Kiloliters to Nanoliters

Dimensional Analysis, Continued Dimensional Analysis: The method of problem-solving that focuses on the units to describe matter. Number of Units being converted x conversion factor to new units = new units unit being converted 2500 cm x.01 m= 25 m 1 cm

Metric Conversions Exa E Petra P Tera T Giga G 10 9 Mega M 10 6 Kilo k 10 3 Hecto h 10 2 Deca da 10 1 Meter / Liter / Gram / Second Deci d Centi C Milli m Micro µ Nano n Pico or Mico Micro µµ Femto f Atto a

In-Class Practice Page 34 Practice Problems 17 a 17 b 17 c 17 d

How Reliable are Measurements? Accuracy and Precision Accuracy: How close a measured value is to an accepted value Precision: How close a series of measurements are to one another

Percent Error The ratio of an error to an accepted value Percent Error = error x 100 accepted value

Significant Figures Include all known digits plus one digit. Usually 2-3 decimal points 5 Primary Rules of Significant Figures 1.Non-zero numbers are always significant 2.Zeros between non-zero numbers are always significant 3.All final zeros to the right of the decimal place are significant 4.Zeroes that act as placeholders are not significant. Instead, convert quantities to scientific notation to remove placeholder zeros. 5.Counting numbers and defined constants have an infinite number of significant figures.

Rounding Off Numbers 4 Primary Rounding Rules, when rounding to 2 significant figures 1.If the digit to the immediate right of the last significant figure is less than five, do not round the last significant figure 2.If the digit to the immediate right of the last significant figure is greater than five, round the last significant figure 3.If the digit to the immediate right of the last significant figure is equal to five and followed by a non-zero digit, round the last significant figure 4.If the digit to the immediate right of the last significant figure is equal to five and is not followed by a non-zero digit, do not round the last significant figure

Rounding Off Numbers, Continued When adding and/or subtracting significant figures, ensure that the final product has the SAME number of significant figures to the right of the decimal point as the add/subtract number with the fewest significant figures WHAT IT MEANS: When adding/subtracting a number with 2 sig figures to the right and 3 sig figures to the right, the final product has 2 sig figures.

In-Class Practice Page 39 Practice Problems 31 a 31 b 32 c 32 d Page 41 Practice Problems 33 a 33 b 34 c 34 d 35 b 36 c

Representing Data Circle Graph or Pie Chart Measure parts of a whole Bar Graph Represents to variables, such as quantity vs. time, quantity vs. temperature or time vs. temperature. Line Graphs Represents the intersection of two sets of data. Slope (y 2 -y 1 ) / (x 2 -x 1 ) Negative Slope: Dependent Variable decreases as the Independent Variable increases Positive Slope: Dependent Variable increases as the Dependent Variable increases