Transcript Measurements and Calculations

Data Analysis
Scientific Method
Not covered in class: Review
What is the Scientific Method?

A logistical approach to solving problems by
observing and collecting data, formulating
hypotheses, testing hypotheses, and
formulating theories that are supported by
data.
Similar chart Fig. 2-3, pg. 31
What’s a hypothesis?
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

A testable statement
Written as an “if/then” statement
Must relate to the experiment that you are
performing

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IF energy is added to a beaker of water in the
form of heat, THEN the water will boil.
NOT if I perform this experiment correctly, I will
get a good grade!
Types of information
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Qualitative-non-numerical data


The sample of copper is shiny
Quantitative-numerical data
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The sample of copper has a mass of 4.7 grams
Qualitative or quantitative?
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The liquid floats on water
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The liquid has a temperature of 55.6°C
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Qualitative
Quantitative
The metal is malleable
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Qualitative
Units of Measurement
Measurements: Number & unit!


Measurements represent quantities such as
volume or length.
Measurements must include a
number and unit!
SI Units
Quantity
Symbol
Base Unit
Abbrev.
Length
Mass
Time
Temp
Amount
l
m
t
T
n
meter
kilogram
second
kelvin
mole
m
kg
s
K
mol
SI Prefixes
Prefix
mega-
Symbol
M
Factor
106
kilo-
k
103
BASE UNIT
---
100
deci-
d
10-1
centi-
c
10-2
milli-
m
10-3
micro-

10-6
nano-
n
10-9
pico-
p
10-12
Derived Units

Combination of base units.

Volume (m3 or cm3)


length  length  length
Density (kg/m3 or g/cm3)

mass per volume
1 cm3 = 1 mL
1 dm3 = 1 L
M
D=
V
Density Example 1

An object has a volume of 825 cm3 and a
density of 13.6 g/cm3. Find its mass.
GIVEN:
WORK:
V = 825 cm3
D = 13.6 g/cm3
M=?
M = DV
M
D
V
M = (13.6 g/cm3)(825cm3)
M = 11,200 g
Density Example 2

A liquid has a density of 0.87 g/mL. What
volume is occupied by 25 g of the liquid?
GIVEN:
WORK:
D = 0.87 g/mL
V=?
M = 25 g
V=M
D
M
D
V
V=
25 g
0.87 g/mL
V = 29 mL
Conversions
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For SI units, you can move the decimal to
convert between prefixes.
Find the difference in the exponents of the 2
prefixes and move the decimal that many
places.

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If the prefix you’re going to is larger, move the
decimal to the left.
If the prefix you’re going to is smaller, move the
decimal to the right.
SI Prefix Conversions
move right
move left
Prefix
mega-
Symbol
M
Factor
106
kilo-
k
103
BASE UNIT
---
100
deci-
d
10-1
centi-
c
10-2
milli-
m
10-3
micro-

10-6
nano-
n
10-9
pico-
p
10-12
SI Prefix Conversion Examples
1) 20 cm =
0.2
______________
m
2) 0.032 L =
32
______________
mL
3) 45 m =
______________
nm
45,000
4) 805 dm =
0.0805
______________
km
Dimensional Analysis
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The “Factor-Label” Method
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Units, or “labels” are canceled, or “factored” out
g
cm 

g
3
cm
3
Dimensional Analysis

Steps:
1. Identify starting & ending units.
2. Line up conversion factors so units cancel.
3. Multiply all top numbers & divide by each bottom
number.
4. Check units & answer.
Dimensional Analysis
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Deriving conversion factors:

If I know that 1 inch is equal to 2.54 cm, then I
can write 2 conversion factors:
1 in = 2.54 cm
=1
2.54 cm 2.54 cm

1 in = 2.54 cm
1=
1 in
1 in
I can use these conversion factors to convert
between inches and centimeters.
Dimensional Analysis Ex. 1
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How many milliliters are in 1.00 quart of
milk?
Starting unit: qt
Ending unit: mL
Equalities: 1 qt=1.057 L, 1 L=1000 mL
Conversion factors:
1 qt
1.057 L 1 L
1000 mL
1.057 L 1 qt
1000 mL 1 L
Dimensional Analysis Ex. 1

Use these conversion factors to convert
between units.
1.00 qt

1L
1000 mL
1.057 qt
1L
= 946 mL
Dimensional Analysis Ex. 2
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You have 1.5 pounds of gold. Find its volume
in cm3 if the density of gold is 19.3 g/cm3.
Starting unit: pounds
Ending unit: cm3
Equalities: 19.3 g=1 cm3, 2.2 lbs=1 kg, 1000 g=1 kg
Conversion factors:
19.3 g 1 cm3 2.2 lbs
1 cm3 19.3 g 1 kg
1000 g
1 kg
1 kg
2.2 lbs 1 kg
1000 g
Dimensional Analysis Ex. 2

Use these conversion factors to convert
between units.
1.5 lb
1 kg
1000 g
1 cm3
2.2 lb
1 kg
19.3 g
= 35 cm3
Dimensional Analysis Ex. 3
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You try!
Temple football needs 550 cm for a 1st
down. How many yards is this?
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Given: 1 in=2.54 cm
550 cm
1 in
1 ft
1 yd
2.54 cm 12 in 3 ft
= 6.0 yd
Dimensional Analysis Ex. 4

A piece of wire is 1.3 m long. How many
1.5-cm pieces can be cut from this wire?
1.3 m
100 cm
1 piece
1m
1.5 cm
= 86 pieces
Using Scientific
Measurements
Accuracy and Precision
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Accuracymeasurement is
close to the “right” or
accepted value
Precision-a set of
measurements are
close to each other
Percent Error
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Represents the accuracy of a measurement.
Can be positive if your value is below the accepted value or
negative if your value is high. (only positive for this class. See note)
NOTE: Please perform percent error calculations with absolute
value. You should NOT have a negative number.
accepted - experimental
% error 
 100
accepted
accepted value
your value
Percent Error Example 1

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.
1.36 g/mL  1.40 g/mL
% error 
 100
1.36 g/mL
% error = -2.9 %
Percent Error Example 2

The actual density of a certain material is
7.44 g/cm3. A student measures the density
of the same material as 7.30 g/cm3. What is
the percent error of the measurement?
7.44 g/mL  7.30 g/mL
% error 
 100
7.44 g/mL
% error = 1.9 %
What are significant figures?

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
Counting Significant Figures

RULES for Counting Sig Figs (Table 2-5, p.47)
1. All nonzero numbers are significant.
ex. 1243 has 4 sig figs
2. Leading zeros with a decimal point are NOT significant
ex. 0.0025 has 2 sig figs
Trailing zeros WITH a decimal ARE significant
ex. 25.00 has 4 sig figs
3. Trailing zeros WITHOUT a decimal ARE NOT
significant
ex. 2,500 has 2 sig figs
Counting Significant Figures Example
23.50
4 sig figs
402
3 sig figs
5,280
3 sig figs
0.080
2 sig figs
Math with Significant Figures

Calculating with Sig Figs
RULE #4:
Multiply/Divide - The # with the fewest sig figs
determines the # of sig figs in the answer.
(13.91g/cm3)(23.3cm3) = 324.103g
4 SF
3 SF
3 SF
324 g
Math with Significant Figures

Calculating with Sig Figs (con’t)
RULE #5:
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  7.9 mL
224 g
+ 130 g
354 g  350 g
Math with Significant Figures
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Calculating with Sig Figs (con’t)
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Exact Numbers do not limit the # of sig figs in
the answer.
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Counting numbers: 12 students
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Exact conversions: 1 m = 100 cm
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“1” in any conversion: 1 in = 2.54 cm
Significant Figures Practice
(15.30 g) ÷ (6.4 mL)
4 SF
2 SF
= 2.390625 g/mL
 2.4 g/mL
2 SF
18.9 g
- 0.84 g
18.06 g  18.1 g
Scientific Notation
65,000 kg  6.5 × 104 kg
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Converting into Sci. Notation:
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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.
Scientific Notation Practice
2,400,000 g
2.4  106 g
0.00256 kg
2.56  10-3 kg
7  10-5 km
0.00007 km
6.2  104 mm
62,000 mm
Proportions
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Direct Proportion
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When one value gets bigger,
the other gets bigger
Ex: mass and volume of a sample
y
y x
x

Inverse Proportion

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When one value gets bigger,
the other gets smaller
Ex: volume and pressure of a gas
1
y
x
y
x