CH. 3 - SCIENTIFIC
MEASUREMENT
3.1
Using and Expressing Measurements
 In
scientific notation, a
given number is written as
the product of two numbers:
a coefficient and 10 raised
to a power.
 The number of stars in a
galaxy is an example of an
estimate that should be
expressed in scientific
notation.
Did You Know?
The mass of an electron is
0.000000000000000000000000000911 g
The mass of the sun is about
2000000000000000000000000000000000 g
Scientific Notation
STOP
Only one digit
3.23 x
4
10
“+” or “-” integer tells
you how many places
to move the decimal
Scientific Notation
 Move
 Ie.
 Move
 Ie.
decimal point to the right if # is small
0.00605 m = 6.05 x 10-3 m
decimal point to the left if # is large
45,000 g = 4.5 x 104 g
Examples
654000 = 6.54 x 105
-3
=
4.56
x
10
.00456
1.23 x 104 = 12,300
3.45 x 10-6 = 0.00000345
Practice Problem A

Convert 0.002001 to scientific notation
2.001 x
-3
10
Practice Problem B

Convert 9.10 x 102 to long form
910
Using Your Calculator…

If you use a…
T.I.
use the “EE” button
Casio use the “Exp” button
Try these now…
(3.9 x 107) x (1.2 x 103)
Practice Problem C

Calculate:
(8.5 x 10-3) - (3.1 x 10-3)
Practice Problem D

Calculate:
(8.4 x 10-3) / (4.7 x 104)

Precision - is a
measure of how
close a series of
measurements
are to one
another

Accuracy closeness of a
measurement to
the true or actual
value of
whatever is
measured
3.1
 To
evaluate the accuracy of a measurement, the
measured value must be compared to the correct value.
To evaluate the precision of a measurement, you must
compare the values of two or more repeated
measurements.
3.1
 Determining



Error
The accepted value is the correct value based on reliable
references.
The experimental value is the value measured in the lab.
The difference between the experimental value and the
accepted value is called the error.
Percent Error
error = actual value - experimental value
Percent error =
| error |
actual value
x 100%
If you estimate that there are 90 jelly beans in a
jar when there is actually 120, your percent
error is…
| 90-120 |
x 100% = 25 % error
120
Practice Problem E

A student estimated the volume of a
liquid in a beaker as 200 mL. When
she poured the liquid into a graduated
cylinder, she measured 208 mL.
Calculate the percent % error.
3.1
Significant Figures in Measurements
 Measurements
must always be reported to the correct
number of significant figures because calculated
answers often depend on the number of significant
figures in the values used in the calculation.They also
convey the degree of accuracy of the measuring
device.
3.1
Significant Figures in Measurements


Suppose you estimate a weight that is between 2.4 lb and 2.5 lb to
be 2.46 lb. The first two digits (2 and 4) are known. The last digit (6)
is an estimate and involves some uncertainty. All three digits convey
useful information, however, and are called significant figures.
The significant figures in a measurement include all of the digits that
are known, plus a last digit that is estimated.
Measuring devices have differing degrees of
accuracy
ignificant Figures
certain digits
6.34 mL
7.00
uncertain digit ( 0.01 mL)
3 significant digits
6.00
Significant Figure’s Rules
1)
Every nonzero digit is significant
2) Leading zeros are never significant
3) Trailing zeros are significant only
after a decimal point (to the right)
4) Zeros between significant
digits are significant
Sig.Fig. Examples
Sig Figs
Scientific Notation
3
2.40 x 10-1 g
0.0034 L
2
3.4 x 10-3 L
24.010 m
5
2.4010 x 101 m
1250 cm3
3
1.25 x 103 cm3
0.240 g
Sig Figs Calculations
•
exact numbers: definitions & whole
numbers (unlimited # of sig.figs.)
12 in/ft
100 cm/m 10 soccer players
2.54 cm/in
2 atoms of O in CO2
Practice Problem F

Round measurements to 3 sig figs

98.473 L
A.
B.
C.
98.4 L
98.5 L
98.0 L
Practice Problem G

Round measurements to 3 sig figs

57.048 m
A.
B.
C.
57.0 m
57.04 m
57.1 m
Practice Problem H

Round each of these measurements to
3 sig figs

1764.9 mL
A.
B.
C.
1765 mL
176 mL
1760 mL
Sig.Figs. Calculations
 multiplication & division:
answer should have the same # of significant
figures as the least # of sig figs
Examples:
9.183 x 1.25 = 11.5 (3 sig.figs.)
2.9 / 21.739 = 0.13 (2 sig.figs.)
Practice Problem I

Correctly round the answer
4.32 cm x 1.7 cm = 7.344 cm2
Sig.Figs. Calculations
addition & subtraction:
answer should have the same # of decimal
places as the least # of decimal places
Examples:
4.02 - 3.956 = 0.06 (2 dec.places)
9.89 + 100 = 110 (0 dec.places)
Practice Problem J

Correctly round the answer
853.20 L - 627.443 L = 225.757 L
INTERNATIONAL
SYSTEM OF
UNITS
SECTION 3.2
S.I. Metric System
Easy to use because it is
based on the number 10

Units of Measurement
Length - meters, m
 Mass - grams, g
 Volume - liters, L
 Time - seconds, s
 Temperature - celcius, oC
 Amount of substance - moles, mol

Volume

For liquids, use a
graduated cylinder
 Measured
in liters (L)
 Milliliters are more
common (mL)

For solids, use math
 Measured
in cubic
centimeters (cm3)
V = l · w · h  cm3
h
l
w
Important Conversions for
Volume
1
3
cm
= 1 mL
&
1 dm3 = 1 L
3.2
Units and Quantities
sugar cube has a volume of 1 cm3. 1 mL is the same as 1
cm3.
A
3.2
A
gallon of milk has about twice the volume of a 2-L
bottle of soda.
Prefix
Symbol
MegaKiloHectoDeka-
M
k
h
dk
SI Unit
d
c
m
µ
n
p
Base Unit
DeciCentiMilliMicroNanoPico-
3 spaces
3 spaces
3 spaces
3 spaces
Practice Problem K

What is the correct SI unit for
temperature?
A.
B.
C.
D.
Kelvin
Fahrenheit
Celsius
None of the Above
Practice problem L

Convert:
250 mL = _____ cm3
3.2

Common metric units of mass include
gram, milligram, and
microgram.
kilogram,
Practice Problem M

Convert:
2.0 x 101 kg = _____ g
Practice Problem N

Convert:
75 mm = _____ km
Practice Problem N

Convert:
99 nm = _____ pm
Temperature


Measures the average kinetic energy of matter
Determines the direction of the heat transfer
 From

high temp. to low temp.
3 temp. scales
 Fahrenheit
 Celcius
 Kelvin
(or absolute)
3.2

Units of Temperature



Temperature is a measure of how hot or
cold an object is.
Thermometers are used to measure
temperature.
Scientists commonly use two equivalent
units, degree Celsius and Kelvin
3.2
 On
the Celsius scale, the freezing point of water is 0°C
and the boiling point is 100°C.
 On the Kelvin scale, the freezing point of water is 273.15
kelvins (K), and the boiling point is 373.15 K.
 The zero point on the Kelvin scale, 0 K, or absolute zero, is
equal to 273.15 °C.
3.2
 Because
one degree on the Celsius scale is equivalent to
one kelvin on the Kelvin scale, converting from one
temperature to another is easy. You simply add or
subtract 273, as shown in the following equations.
Temperature Conversions
K = °C + 273
°C = K - 273
°C =(°F - 32)/1.8
°F = (1.8x°C) + 32
Practice Exercises
Normal human body temperature is 37 °C . What is
That temperature in kelvins?
K = °C + 273 K = 37 + 273 K = 310
Surgical instruments may be sterilized by heating at
443 K for 1.5 hours. Convert kelvins to °C.
°C = K - 273 °C = 443 - 273 °C = 170
Practice Problem
Average temperature of Colorado in October is
18.3°C. What is this in °F?
3.3
Conversion
Factors
Section 3.3

Conversion Factors
 What
happens when a measurement is multiplied by a
conversion factor?
3.3
A
conversion factor is a ratio of equivalent
measurements.
 The ratios 100 cm/1 m and 1 m/100 cm are
examples of conversion factors.
3.3
***Remember***
 When
a measurement is multiplied by a conversion
factor, the numerical value is generally changed, but
the actual size of the quantity measured remains the
same.
3.3
 The scale of the micrograph is in nanometers.
Using the relationship 109 nm = 1 m, you can
write the following conversion factors.
3.3
Dimensional Analysis
 Dimensional
analysis is a way to analyze and solve
problems using the units, or dimensions, of the measurements.

Dimensional analysis provides you with an alternative
approach to problem solving.
Practice Problem
Practice Problem
Practice Problem
3.3

Converting Complex Units
 Many
common measurements are expressed as a ratio
of two units. If you use dimensional analysis, converting
these complex units is just as easy as converting single
units. It will just take multiple steps to arrive at an
answer.
Practice Problem

Section 3.4

Density is mass per unit volume
D = mass / volume

The higher the density the more “stuff”
is packed together
3.4
Determining Density

Density is an intensive property that depends only on the
composition of a substance, not on the size of the sample.

If the density of an object is less than the
density of the fluid it is in, it will float in
that fluid.
 Ex.
Oil and Water = the oil floats
Rock and Water = the rock
sinks
Practice Exercises
A piece of silver jewelry has a mass of 8.37 g.
If the density of silver is 10.5 g/cm3, what is
the volume of the piece of jewelry?
V=M/D
V = 8.37 g / 10.5 g/cm3
V = 0.797 cm3
Peanut oil has a density of 0.92 g/cm3. If a
recipe calls for 237 mL of peanut oil, what
mass are you using?
M=VxD
M = 237 mL x 0.92 g/cm3
M = 220 g
Practice Problem

Calculate the volume of a gas that
has the measurements of 25 g and
2.0 g/mL

Specific Gravity
The
ratio of the density of a
substance to the density of water
(1 g/cm3)
Measured with a hydrometer
No units
Specific Gravity Example:
Material
Gold
Density @
20 oC
19.3 g/cm3
Aluminum
2.70 g/cm3
Corn Oil
0.922 g/cm3
Specific
Gravity
19.3
2.70
0.922