2 Analyzing Data
BIGIDEA
Write the Big ldea forthis chapter.
Use the "What I Know" column to list the things you know about the Big ldea. Then list the
questions you have about the Big ldea in the"What I Want to Find Out"column. As you read the
chapter, fill in the"What I Learned"column.
KWL
What I Know
What
lwontto
Find
Out
Science Notebook. Analyzing Data
17
Whot t Learned
2 Analyzing Data
1 Units and Measurements
tETl2(H)
MAIN
IDTA
Write the Main ldea for this lesson.
G=vretr V*ceguL*av
Recall the definition of the ReviewVocabulary term.
mass
ma55
*l*w Uoe*Bs,"sRy
Defi ne each New Vocabulary term.
base unit
base unrt
derived unit
density
derived unfr
deyinl
Match the Sl base units below with their functions.
distance
16'
temperature
@
=
o
kilogram
:
time
T
h
e
kelvin
mass
liter
volume
_
Science Notebook. Analyzing Data
I8
o
1 Units and Measurements
Use
with pages 32-37.
(continued)
ldentify five items around your home that
use Sl units of measurement.
1
Unrls
2,
3.
4.
5.
Ease Unts and 5l
Pretixes
Sequence these prefixes from smallest to largest.
,_,_-_
ptco
-
micro
----
--- -
nano
mitli
deci
kilo
,
giga
---*--*-
centi
mega
Compare and contrast the Kelvin scale and the Celsius scale.
E
e€f
E
E
lT? lnfer Which
is
warmer, 25'F or 25"C?
-t
g
u
E
@
e
Derived Untls
Explain density by completing the following statement and equation.
Density is a
object to its
that
---
the
-----
-----.-
of an
-- --
density:
&Ef ffi?
State the quantitiesthat must be known in order to calculate
density.
Science Notebook. AnalYzing Data
19
1
Units and Measurements (continued)
Use
with page 38.
Solve
Read Example Problem 1 in your text.
Usiog Dens'rty and
Yolumeto Find Mass
Problem
Determine the mass of an object that, when placed in a 25-mL graduated
cylinder containing 14 mL of water, causes the level of the water to rise to
19 mL. The object has a density of 3.2 g/mL.
1. Analyze the Problem
Known:
Unknown:
You know the density and the volume of an object and must determine
its mass; therefore, you will calculate the answer using the density
equation.
2.
Solve for the Unknown
Write the density equation.
Rearrange the density equation to solve for mass.
Substitute the known values for
into the equation.
and
E
=.
Multiply the values and units. The mL units will cancel out.
mass:
3.
x
:
o
=
6l
d
E
I
=
m
Evaluate the Answer
3.
a
The two sides of the equation should be
densitY =
lf you divide 16 g by 5.0 mL, you get
Science Notebook. Analyzing Data
20
1 Units and Measurements
(continued)
REVIEW IT!
4.
Define the Sl units for length, mass, time, and temperature.
5. Descibe how adding
6.
the prefix mega- to a unit affects the quantity being described.
Compare a base unit and a derived unit, and list the derived units used for density and
volume.
7. Define the relationships
8. Apply
among the mass, volume, and density of a material.
Why does oilfloat on water?
9. Calculate
Samples A, B, and C have masses of 80 g, 12 g, and 33 g, and volumes of
20 mL, 4 cm3 , and 1 1 mL, respectively. Which of the samples have the same density?
c
.e
!r
E
c
(j,
to. Design a concept map that
shows the relationships among the following terms:
volume, derived unit, mass, base Ltnit, time, and length.
E
o
s
.9t
o
,o
Science Notebook. Analyzing Data
27
2 Analyzing Eata
2
Scientifie Notation and Dimensional
ffi2(C),2(H)
Anaffis
MAIIUIDEA
Write the Main ldea for this lesson,
MHrenuu*u
Recall the
definitisn of the ReviewVocabulary term.
quantitative data
quarrfttafrve dala
ffiffi*s*a*ay
Defirte eaeh New Vocabulary term.
scientific notation
seierirtic notation
dimensionaI analysis
conversiort factor
dimensionat anatysis
conversion tactor
*remfu*xas*,p
Define the following term.
5um
sum
6
@
3
a
+
c
G
Science Notebook. AnalyzinE Data
22
2
Scientific Notation and Dimensional Analysis
Use
with page 41.
Solve Read Example Problem
(continued)
2 in your text.
Soieolrlio Notation
Problem
Change the following data into scientific notation:
a. The distance between Pluto and the Sun
b.
is 5,913,000 km.
The density of nitrogen gas, a major component of Pluto's
atmosphere, is 0.001 2506 g/cm3.
1. Analyze the Problem
Known:
Unknown:
You are given
two measurements. ln both cases, the answers will be
1 and 1 0 that are multiplied by a power of ten.
factors between
2.
Solve for the Unknown
Move the decimal point to produce a factor between 1 and 10. Count
the number of places the decimal point moved and the direction.
a.
The
b.
decimalpoint moved
The
places to the
decimalpoint moved
places to the
Remove the extra zeros at the end or beginning of the factor.
Multiply the result by 10n where n equals the
c
o
E
.
number. When the decimal point moves to the right,
g
Ig
t9
When the decimal point moves to the left, n is a
nisa
number. Remember to add units to the answers.
E
@
I
a.
.E
e
0
b.
3. Evaluate the Answer
have
between
and
The answers
to Pluto
factors. The first factor is a number
is a large number, 10 has
.
a
ln answer a, because the distance
exponent. In answer b,
because the density of nitrogen gas is a very small number, the
exponent is
Science Notebook. Analyzing Data
23
2
Scientific Notation and Dimensional Analysis
Use
with
pages 42,46.
(continued)
Restate the process used to add two numbers that are
expressed in scientific notation.
Soieotttio Notation
Using Ctnversion
Faolors
Solve Read Example Problem 4 in your text.
Problem
The Cassini probe heading toward Saturn will reach speeds of
5.2 kilometers per second. How many meters per minute would it travel
at this speed?
1. Analyze the Problem
Known:
Unknown:
You need conversion factors that relate kilometers to meters and seconds
to minutes. A conversion factor
of
is a
used to express
2.
tn
Solve for the Unknown
to meters. Set up the conversion factor so that
First convert kilometers
out.
5.2km-1000m_ m
'=
the kilometer units will cancel
5
f k,
-
g
A
E
5
Next convert seconds to minutes. Set up the conversion factor so
the seconds will cancel
out.
5200m- 60s
,
3.
t]Ttill -
m
mil1
Evaluate the Answer
To check your answer, you can do the steps in reverse order.
5.2km.-
s
60s 312km..1000m
1 min
min km
Science Notebook. Analyzing Data
24
I
E
m
min
that
=
H
[.
I
2 Scientific Notation
and Dimensional Analysis (continued)
&.6V[E*' rr!
24. Describe how scientific notation
makes it easier to work with very large or very small
numbers.
25. Express the numbers
0.00087 and 54,2A0,000 in scientific notation.
26. Write the measured distance quantities 3 x
10-4 cm and 3
x
104 km in regular
notation.
27. Write a conversion factor relating cubic centimeters and milliliters.
28. Solve How many millimeters
29. Explain
are there in 2.5
x 102 km?
how dimensional analysis is used to solve problems.
E
,t
r
Ig
ro. Apply Concepts
A classmate converts 68 km to meters and gets 0.068 m as the
answer. Explain why this answer is incorrect, and identify the likely source of the error.
u
E
@
'-o
o
0
U
31. Organize Create a flowchart that outlines when to use dimensional
to use scientific notation.
Science Notebook. Analyzing Data
25
analysis and when
2 Analyzing Data
3
Uncertainty in Data
IItSl2(F), 2(G), 2(H)
$we*ru rnrA
Write the Main ldea for this lesson.
*sa*=w
H*****r**v
Recall the
definition of the Review Vocabulary term.
experiment
experiment
*luw E+<*s131f,*Y
Define each New Vocabulary term.
accuracy
accuracY
precision
error
precision
percent error
significant figure
err0r
percent error
signiticarft tigure
Science Notebook. Analyzing Data
26
3
Uncertainty in Data
Use
with pages 48-49.
(continued)
Explain percent error by completing the statement and equation below.
_ _ -_ _ - of an
Percenterror:
Percent error is the
Aoouraoy aod Preoision
_ to an
x 100
SHf ffi? Summarize why error is important.
Solve Read Example Problem 5 in your text.
YS{.J TR.Y j"r.
Problem
C,aloulatrng Peroent
wr0r
Calculate the percent errors. Report your answers to two places after the
decimal point.The table below summarizes Student Bt data.
trial
i
i
Density
(g/cm3;
1.68
1.45
2
i
Etrot
1g/cm3)
i
,..
0.09
-0.14
1. Analyze the Problem
Known:
Unknown:
Use the accepted value for density and the errors to calculate percent error.
pc
E
E
B
2.
Solve for the Unknown
Substitute each error into the percent error equation.
=*
X 100
oerCenterrgr:
'
accepted value
x 100: T---l
percent error :
g
I
E
@
'io
uo
1.59 g/cm3
percent error
100
:
x lOO:
1.59
percent error
'
3.
:
= ------- , x
g/cm'
1.59 g/cm3
f--l
Evaluate the Answer
The percent error is greatest for trial __
and smallest for
trial
--
,
largest error,
which was closest to the accepted value.
Science Notebook. AnalYzing Data
27
_ which had the
3
Uncertainty in Data
Use
with pages 50-52.
gigoi ioarfi Figures
(continued)
tdentify the significant numbers below by drawing a circle around them.
Use the five rules for recognizing significant digits on page 51 for
reference.
325,078
0.025
Qouotliog Numbers
5600
Explain the rules for rounding numbers by completing the following
sentences. Then complete the example of each rule for rounding
numbers.
1. lf the digit to the immediate right of the last significant figure is less
than five,
_
3.751
2. lfthedigitto
the immediate right ofthe last significantfigure is
greater than five,
4.127
3. lf the digit to the immediate right of the last significant figure is
equal to five and is followed by a nonzero digit,
8.3253
4, lf the digit to the immediate right of the last significant figure is
equal to five and is not followed by a nonzero digit, look at the
0
E
qa
o
last significant figure.
=
6)
E
-f
1.4750 =
_____;
1.4650
=
m
=
A
c
o
REVIEW IT!
45. State how a measured
value is reported in terms of known and estimated digits.
Seience Notebook. Analyzing Data
2A
3
Uncertainty in Data
46. Define
(continued)
accurocy and precision.
47. ldentify the number
of significant figures in each of these measurements of an object's
length: 76.48 cm,76.47 cm, and 76.59 cm.
48. Apply
The object in Question 47 has an actual length of 76.49 cm. Are the
measurements in Question 47 accurate? Are they precise?
49. Calculate the error and percent
error for each measurement in Question 47.
50. Apply Write an expression for the quantity
506,000 cm in which it is clear that all the
zeros are significant.
g
group of coins. The mass of a single
E
- St. Analyze Data Students collected mass data for a
.oin is 5.00 g. Determine the accuracy and precision of the measurements.
t
E
=
@
5
Number of
o
I
Mass
(g)
coins
20
30
5
10
23.2 54.5 105.9 154.5
Science Notebook. Analyzing Data
29
50
246.2
2 Analyzing
4
Data
Representing Data
@2(G),2(H)
MAINIDEA
Write the Main ldea tor this lesson.
Rfftrlg Yoc*rura*r
Recall the definition of the ReviewVocabularyterm.
independent variable
inde?enderrt variable
Itnw YacrBEr.*RV
Defi ne each New Vocabulary term.
graph
qraPh
Science Notebook. Analyzing Data
30
Use
with pages 55-56.
Draw and label (a) a circle graph and (b) a bar graph using the
information in the table below.
Qraphing
Student Budget
Budget items
Percent
Car insurance
45
Movies
6
Books
5
Clothing
30
Miscellaneous
4
Gas
10
Student Budget bar graph
Student Budget circle graph
best displays the data in the Student Budget
table because
AeTff?
Analyze What percent of the chlorine sources are natural?
What percent are manufactured compounds?
Science Notebook. Analyzing Data
31
4
Representing Data (continued)
Use
with pages 56-57.
Atr fi? lnterpret Which two food servings provide equalamounts of
magnesium?
Graghiog
ldentify each of the following slopes.
slope
slope
/'
\
.'"'
Analyze whether the following sequences will likely plot as linear or
nonlinear relationships.
SequenceA:
Result 1:2
Result 2:4
Result 3: 7
Result 4: 10
Answer:
A*
SequenceB:
Result A:31
Result B:27
Result C:49
Result D: 45
Answer:
[T-? tdentify the graph that shows a direct
relationship.
€
,
,3
@
3
a
f-
=
m
c
c
s0
t
Science Notebook. Analyzing Data
32
4
Representing Data (continued)
Use
with pages 57-58.
Organize information about interpreting graphs by completing the
sentences below.
lntergreling Sraphs
types of
lnformation on a graph typically consists of
variables:
variables and
, -_
variables.
The relationship between the variables may reflect either a
ora
slope.
When reading the graph, you use either interpolation for
or-
for estimated
values beyond the plotted points.
Gtr
[T-? Explain why extrapolation might be less reliable than
interpolation.
A€T
[T-? tnterpret By how much did the total ozone vary during the
9-month period shown for 1979-2010?
c
€
I
a
!
4
*
REVIEW fT!
E
E
52. Explain why graphing can be an important tool for analyzing
o
data.
!
o
o
o
Science Notebook. Analyzing Data
B3
4
Representing Data (continued)
What type of data must be plotted on a graph for the slope of the line to
represent densitY?
53. lnfer
54. Relate
lf a linear graph has a negative slope, what can you say about the dependent
variable?
55. Summarize What data are best displayed on a circle
55. Construct
a circle graph for
0.040/o CO2 and
the composition of air:
graph? On a bar graph?
78.08o/o N, 20.95016 A2,0.93o/o Ar,
and
other gases.
to
:.
o
57. lnfer from
@
Figure 17 how long the ozone hole lasts.
3
6
I
il
o
=
Apply
On a separate sheet of paper, graph mass versus volume for the data given in
the table. What is the slope of the line?
---*-T
', t2 i
7.s
I volume (cm3)
liil
;lili -- -. - "* -- - -*- * * * "l'------i--.--'!
-.
l:irii
r Mass
:a.S
i
-
-
(g)
".
r
s i zz
:
-
i 24j I
I
+S.O
1
Science Notebook. Analyzing Data
?4
70.1
i
o