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

Second

Meter

Kilogram

Kelvin

Derived unit

Liter

Density

Mass

Measurement

WHAT IS A MEASUREMENT?Comparison between an unknown and a standard.

SI & BASE UNITS Systeme Internationale d’Unites

(SI) –

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 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=𝑚𝑎𝑠𝑠𝑣𝑜𝑙𝑢𝑚𝑒

𝐷=𝑚𝑉

DENSITY SAMPLE PROBLEM 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)

SUBSTITUTION (Substitute in numbers with units)

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 0.925 g/mL. What is the volume of the sunflower oil in mL?

m = 116 g

V = ? mL

D = 0.925 g/mL

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:

V

MD

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 gV

MD

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/mLV = ? mLM = 25 g

WORK:

V

MD

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/mLV = ? mLM = 25 g

WORK:V = M D

V = 25 g

0.87 g/mL

V = 29 mLV

MD

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

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

Converting into Sci. Notation:Move decimal until there’s 1 digit to its left. Places moved = exponent.

Large # (>1) positive exponentSmall # (<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 0.000023

SCIENTIFIC NOTATION – PRACTICE PROBLEMS

1) 2,400,000 g

2) 0.00256 kg

3)7 10-5 km

4)6.2 104 mm

SCIENTIFIC NOTATION – PRACTICE SOLUTIONS

1) 2,400,000 g

2) 0.00256 kg

3)7 10-5 km

4)6.2 104 mm

2.4 106 g

2.56 10-3 kg

0.00007 km

62,000 mm

Convert the following to proper scientific notation

SCIENTIFIC NOTATION – ADDITION & SUBTRACTION

In order to add or

subtract numbers

written in scientific

notation, the

exponents must be

the same!!!

SCIENTIFIC NOTATION: MULTIPLICATIONMultiply 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) =

5.44EXPEXP

EEEE÷÷

EXPEXP

EEEE ENTERENTER

EXEEXE7 8.1 4

= 671.6049383= 670 g/mol= 6.7 × 102 g/mol

Type on your calculator:

DIMENSIONAL ANALYSISDimensional 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

4800 g to kg

5600 dm to m

72 g to mg

2.45 x 102 ms to s

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?

VOCABULARYAccuracy Precision Error

Percent Error Significant Figure

BAKING COOKIESWhat are some of the measurements required in making cookies?

Cup, tablespoon, Teaspoon.

BAKING COOKIESWould 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!!!!

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

Indicates accuracy of a measurement

100literature

literaturealexperimenterror %

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.

100g/mL 1.36

g/mL 1.36g/mL 1.40error %

% error = 2.90 %

SIGNIFICANT FIGURES

Indicate precision of a measurement.

Recording Sig FigsSig figs in a measurement include the known digits plus a final estimated digit

SIGNIFICANT FIGURES

Indicate precision of a measurement.

Recording Sig FigsSig 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

4. 0.080

3. 5,280

2. 402

1. 23.50

SIGNIFICANT FIGURESCounting Sig Fig

Examples1. 23.50

2. 402

3. 5,280

4. 0.080

4. 0.080

3. 5,280

2. 402

1. 23.50

SIGNIFICANT FIGURESCounting Sig Fig

Examples1. 23.50

2. 402

3. 5,280

4. 0.080

4 sig figs

3 sig figs

3 sig figs

2 sig figs

SIGNIFICANT FIGURES Calculating with Sig FigsMultiply/Divide - The # with the fewest sig figs determines the # of sig figs in the answer.

(13.91g/cm3)(23.3cm3) = 324.103g

324 g

4 SF 3 SF3 SF

SIGNIFICANT FIGURES

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+ 4.1 mL 7.85 mL

224 g+ 130 g 354 g 7.9 mL 350 g

3.75 mL+ 4.1 mL 7.85 mL

224 g+ 130 g 354 g

SIGNIFICANT FIGURES

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

SIGNIFICANT FIGURES: PRACTICE PROBLEMS5. (15.30 g) ÷ (6.4 mL)

= 2.390625 g/mL

18.1 g

6. 18.9 g- 0.84 g18.06 g

4 SF 2 SF

2.4 g/mL2 SF

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

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. 0.10 %

B. 0.20 %

C. 10 %

D. 20 %

PERCENT ERROR: PRACTICE QUESTION

SECTION 4: REPRESENTING DATA

ESSENTIAL QUESTIONS & VOCABULARYWhy 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 VARIABLESOn 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 GRAPHSInterpolation 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.