 # Chapter 2: analyzing data

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Chapter 2: analyzing data
Mrs. Faria

Do Now: Hand in the Measuring activity – front of the room!!
Identify different quantities that can be measured and their units of measurement.

Essential Questions What are the SI base units for time, length, mass, amount of substance and temperature? How does adding a prefix change a unit? How are the derived units different for volume and density?

Vocabulary Base unit Derived unit Second Liter Meter Density Kilogram
Mass Kelvin Measurement

What is a measurement? Comparison between an unknown and a standard.

SI & Base units Systeme Internationale d’Unites (SI) – Base Units
An internationally agreed upon system of measurements. Base Units Defined unit in a system of measurement that is based on an object or event in the physical world, and is independent of other units.

Base units Time – second Distance – Meter Mass – kilogram
Based on the frequency of radiation given off by a cesium-133 atom Distance – Meter Distance light travels in a vacuum in 1/299,792,458th of a second. Mass – kilogram Actual mass of 1 kilogram (see picture) Temperature – Kelvin Zero Kelvin (absolute zero) refers to the point where there is virtually no particle motion or kinetic energy. Two other commonly used scales; Fahrenheit and Celsius.

SI prefixes SI Prefixes are multipliers that precede the base unit.
You must know the three that are outlined.

Derived units Not all quantities can be measured with SI base units.
Derived Units – a unit that is defined as a combination of base units. Speed – The SI unit for speed is m/s (measurement of distance divided by time) Volume – SI unit for volume is cm3.

volume 1 mL – volume of liquid that occupies a 1cm x 1cm x 1cm cube
1 mL = 1 cm3 QUESTION – How many mL in a 1m x 1m x 1m (1m3) box?

Density Density – derived unit that describes the amount of mass per unit of volume. g/cm3 g/mL Kg/L 𝐷𝑒𝑛𝑠𝑖𝑡𝑦= 𝑚𝑎𝑠𝑠 𝑣𝑜𝑙𝑢𝑚𝑒 𝐷= 𝑚 𝑉

Density Sample Problem
When a piece of aluminum is placed in a 25-mL graduated cylinder that contains 10.5 mL of water, the water level rises to 13.5 mL. What is the mass of the aluminum? (density of aluminum is 2.7 g/mL). GIVEN (variable, number, units) V = 3 mL D = 2.7 g/mL UNKNOWN (variable, question mark, units) m = ? g FORMULA (no need to rearrange formula) D= m V SUBSTITUTION (Substitute in numbers with units) 𝟐.𝟕 𝒈 𝒎𝒍 = 𝒎 𝟑 𝒎𝑳 SOLUTION (Variable, number, units) m = 8.1 g

Sample Problem #2 Question 116 g of sunflower oil is used in a recipe. The density of the oil is g/mL. What is the volume of the sunflower oil in mL? m = 116 g V = ? mL D = g/mL 𝐷= 𝑚 𝑉 0.925 𝑔 𝑚𝐿 = 116 𝑔 𝑉 V = 125 mL

Density- Practice Problem 1
An object has a volume of 825 cm3 and a density of 13.6 g/cm3. Find its mass. GIVEN: V = 825 cm3 D = 13.6 g/cm3 M = ? g WORK:

Density – Practice Problem 1 Solution
An object has a volume of 825 cm3 and a density of 13.6 g/cm3. Find its mass. GIVEN: V = 825 cm3 D = 13.6 g/cm3 M = ? g WORK: M = DV M = (13.6 g/cm3)(825cm3) M = 11,200 g

Density – Practice Problem 2
A liquid has a density of 0.87 g/mL. What volume is occupied by 25 g of the liquid? GIVEN: D = 0.87 g/mL V = ? mL M = 25 g WORK:

Density – practice Problem 2 SOlution
A liquid has a density of 0.87 g/mL. What volume is occupied by 25 g of the liquid? GIVEN: D = 0.87 g/mL V = ? mL M = 25 g WORK: V = M D V = g 0.87 g/mL V = 29 mL

Section 2: Scientific Notation & Dimensional Analysis

Essential questions & vocabulary
Why use scientific notation to express numbers? How is dimensional analysis used for unit conversions? VOCABULARY Scientific notation Dimensional analysis Conversion factor

5,450,000  5.45 x 106 Scientific notation
Used to express any numbers as a number between 1 and 10 multiplied by 10 raised to a power. 5,450,000  5.45 x 106 Exponent Coefficient

Scientific Notation 65,000 kg  6.5 × 104 kg
Converting into Sci. Notation: Move decimal until there’s 1 digit to its left. Places moved = exponent. Large # (>1)  positive exponent Small # (<1)  negative exponent Only include sig figs. 65,000 kg  6.5 × 104 kg

Scientific notation Positive Power – number larger than 1
2.3 x 105  230,000 Negative power – number smaller than 1 2.3 x 10-5 

Scientific Notation – Practice Problems
1) 2,400,000 g 2) kg 3) 7  10-5 km 4) 6.2  104 mm

Scientific Notation – Practice Solutions
Convert the following to proper scientific notation 1) 2,400,000 g 2) kg 3) 7  10-5 km 4) 6.2  104 mm 2.4  106 g 2.56  10-3 kg km 62,000 mm

Scientific Notation – Addition & Subtraction
In order to add or subtract numbers written in scientific notation, the exponents must be the same!!!

scientific notation: Multiplication
Multiply the coefficients Use properties of exponents to multiply the power of 10 Simplify

Scientific Notation: Division
Divide the coefficients. Use properties of exponents to multiply the power of 10 Simplify

Scientific Notation- Calculations
(5.44 × 107 g) ÷ (8.1 × 104 mol) = Type on your calculator: EXP EE EXP EE ENTER EXE 5.44 7 8.1 ÷ 4 = = 670 g/mol = 6.7 × 102 g/mol

Dimensional Analysis Dimensional Analysis: systematic approach to problem solving that uses conversion factors to move, or convert from one unit to another. Conversion Factor: ratio of equivalent values having different units.

Dimensional analysis: practice
360 s to ms 72 g to mg 4800 g to kg 2.45 x 102 ms to s 5600 dm to m 5 g/cm3 to kg/m3

Section 3: Uncertainty in data

Essential Questions & Vocabulary
How do accuracy and precision compare? How can the accuracy of experimental data be described using error and percent error? What are the rules for significant figures and how can they be used to express uncertainty in measured and calculated values? VOCABULARY Accuracy Percent Error Precision Significant Figure Error

BAKING COOKIES What are some of the measurements required in making cookies? Cup, tablespoon, Teaspoon.

Baking Cookies Would a batch of cookies turn out ok if all ingredients would be measured in teaspoons? NO!!! = too much error would build up. It is important to select appropriate measurement instruments based on the amounts needed!!!!

ACCURATE = CORRECT PRECISE = CONSISTENT
Accuracy vs. Precision Accuracy - how close a measurement is to the accepted value Precision - how close a series of measurements are to each other ACCURATE = CORRECT PRECISE = CONSISTENT

Percent Error your value accepted value
Indicates accuracy of a measurement your value accepted value

Percent Error - Example
A student determines the density of a substance to be 1.40 g/mL. Find the % error if the accepted value of the density is 1.36 g/mL. % error = 2.90 %

Significant Figures Indicate precision of a measurement.
Recording Sig Figs Sig figs in a measurement include the known digits plus a final estimated digit

Significant Figures 2.35 cm Indicate precision of a measurement.
Recording Sig Figs Sig figs in a measurement include the known digits plus a final estimated digit 2.35 cm

Significant Figures Count all numbers EXCEPT: Leading zeros -- 0.0025
Trailing zeros without a decimal point -- 2,500

Counting Sig Fig Examples
Significant Figures Counting Sig Fig Examples 3. 5,280 3. 5,280

Counting Sig Fig Examples
Significant Figures Counting Sig Fig Examples 4 sig figs 3 sig figs 3. 5,280 3. 5,280 3 sig figs 2 sig figs

Significant Figures (13.91g/cm3)(23.3cm3) = 324.103g 324 g
Calculating with Sig Figs Multiply/Divide - The # with the fewest sig figs determines the # of sig figs in the answer. (13.91g/cm3)(23.3cm3) = g 4 SF 3 SF 3 SF 324 g

Significant Figures 3.75 mL + 4.1 mL 7.85 mL 3.75 mL + 4.1 mL 7.85 mL
Calculating with Sig Figs (con’t) Add/Subtract - The # with the lowest decimal value determines the place of the last sig fig in the answer. 3.75 mL mL 7.85 mL 3.75 mL mL 7.85 mL 224 g + 130 g 354 g 224 g + 130 g 354 g  7.9 mL  350 g

Significant Figures Calculating with Sig Figs (con’t)
Exact Numbers do not limit the # of sig figs in the answer. Counting numbers: 12 students Exact conversions: 1 m = 100 cm “1” in any conversion: 1 in = 2.54 cm

Significant figures: practice problems
5. (15.30 g) ÷ (6.4 mL) 4 SF 2 SF  2.4 g/mL 2 SF = g/mL g g 18.06 g  18.1 g

Practice Question Determine the number of significant figures in the following: 8,200, 723.0, and 0.01. A. 4, 4, and 3 B. 4, 3, and 3 C. 2, 3, and 1 D. 2, 4, and 1

Percent Error: Practice Question
A substance has an accepted density of 2.00 g/L. You measured the density as 1.80 g/L. What is the percent error? A % B % C. 10 % D. 20 %

Section 4: Representing Data

Essential questions & Vocabulary
Why are graphs created? How can graphs be interpreted? VOCABULARY Graph Interpolation Extrapolation

Graphing A graph is a visual display of data that makes trends easier to see than in a table. A circle graph, or pie chart, has wedges that visually represent percentages of a fixed whole.

GRAPHING – bar graphs Bar graphs are often used to show how a quantity varies across categories.

Graphing – dependent & independent variables
On line graphs, independent variables are plotted on the x-axis and dependent variables are plotted on the y-axis.

Graphing – finding the slope
If a line through the points is straight, the relationship is linear and can be analyzed further by examining the slope.

Interpreting graphs Interpolation is reading and estimating values falling between points on the graph. Extrapolation is estimating values outside the points by extending the line. This graph shows important ozone measurements and helps the viewer visualize a trend from two different time periods.