Chapter 1:
Nature Of Measurement
INTRODUCTION
 Measurement : quantitative observation consisting of
number and scale (unit))
 Examples:
 length: 2.2 m
 force: 4.45 kg m/s2
SI UNITS
 International System of Unit (Système Internationale
d’Unites)
 Based on metric system (?)
 Is a decimal system of units for measurements of mass,
length, time and other quantities which can be built from
7 base units:
SI BASE UNITS
Measurement
Unit
Symbol
meter
m
Mass
kilogram
kg
Time
second
s
kelvin
K
Mol
Mol
Electrical current
ampere
A
Luminous intensity
candela
cd
Length
Temperature
Amount of substance
SI PREFIX
Prefix
Meaning
Symbol
Factor
value
1012
109
106
103
1000000
1000
tera
giga
mega
kilo
millions of
thousands of
T
G
M
k
deci
tenths of
d
10-1
0.1
centi
hundredths of
c
10-2
0.01
milli
thousandths of
m
10-3
0.001
micro
millionths of

10-6
0.000001
nano
billionths of
n
10-9
0.000000001
pico
trillionths of
p
10-12
0.000000000001
Quantities differing from the base unit by powers of ten are
noted by the use of prefixes.
COMMON UNITS USED IN
LABORATORY MEASUREMENTS
-LENGTH
-MASS
-TEMPERATURE
-VOLUME
LENGTH
 The SI unit for length, the meter (m) is too large for
most laboratory purposes.
 More convenient units are the centimeter (cm) and
millimeter (mm).
1 cm = 10-2 m = 0.01 m
1 mm = 10-3 m = 0.001 m
1 m = 100 cm = 1000 mm
1 cm = 10 mm
MASS
 Def.: amount of matter in an object
 SI unit for mass: kilogram (kg)
 But the more convenient is gram (g) used for most
laboratory measurement.
1 kg = 1000 g
1g = 1000 mg
1 mg = ? G
1 g = ? g
TEMPERATURE
 SI unit: Kelvin
 usually measured with a thermometer
 Three common scales:
degrees Celsius = oC
Kelvin = K
degrees Fahrenheit = oF
 Mathematical formulas to convert:
K = oC + 273
oC = K - 273
oF = (1.8 x oC) + 32
VOLUME
 Is derived unit with dimensions of (length)3
 Unit: m3
 In chemistry, usually we measure amount of liquids. The
traditional metric unit of volume: liter (L)
1 L = 1000 cm3
1L=
_?_
m3
 the glassware we normally use is marked in milliliters
(mL)
1 L = 1000 mL
1 mL = 1cm3
DERIVED UNITS
Measurement
Definition
Symbol
Area
Length x width
m2
density
Mass/volume
kg/m3
Speed
Distance / Time
m/s
Acceleration
Change in speed / Time
m/s2
Force
Mass x Acceleration
(kg.m)/s2
(newton, N)
pressure
Force/area
kg/(m.s2)
Pascal, Pa
energy
Force x length
(kg.m2)/s2
Joule, J
60 min in one hour
60 min PER hour
60 min
1hour
and
PER
expression
1hour
60 min
60 minutes = 1 hour
 Conversion factor is written as a fraction
 Conversion factors:
60 min
1hour
and
1hour
60 min
a) how many minutes in 2.72 hours?
60 min
2.72 hours x
1hour
= 163 minutes
b) how many hours in 250 minutes?
259 min x
1hour
60 min
= 4.32 hours
Example 1:
Perform the following conversions
a) 255 nm = ? cm
b) 0.12 kg = ? cg
c) 1 L = ? dm3
a) 255 nm = ? cm
SI prefix:
1nm = 1 x 10-9 m
1m = 100cm
Conversion factor:
1nm
and
1 x 10-9 m
100cm
1m
1 x 10-9 m
1nm
and
1m
100cm
nm
255 nm x
cm
1 x 10-9 m
1nm
= 2.55 x 10-5 cm
x
1cm
1 x 10-2 m
b) 0.12 kg = ? cg
(0.12 kg)
1 x 103 g
1kg
= ?
1cg
1 x 10-2 g
c) 1 L = ? dm3
1 L = 1000 mL = 1000 cm3
1000 cm3 x
1000
cm3
x
1m
100 cm
1 m3
1 x 106 cm3
3
x
1dm
3
1 x 10-1 m
x
1dm3
1 x 10-3 m3
= ? dm3
Exercise 1:
The block of wood pictured below has a mass of 2.52 kg.
What is the density of the wood in g/cm3
6.2 cm
5.1 cm
1.08 m
Solution
 Change the mass from kg to g
 Change the length from m to cm
 The volume of the wood:
 The density of the wood:
Exercise 2:
1. Perform the following conversions:
a) 0 oC to oF and K
b) 100 oC to oF and K
2. The average density of earth is 5.52 g/cm3. What is
its density in kg/m3
Answer:
Homework
An empty vial weights 55.32 g.
1) If the vial weights 185.56 g when filled with liquid
mercury (d = 13.53 g/cm3), what is its volume?
2) How much would the vial weight if it were filled with
water?
ACCURACY AND PRECISION
Accuracy:
 how close a measurement is to the true value of
the quantity that was measured.
Precision:
 how closely two or more measurements of the
same quantity agree with one another
 can be judge by examining the average of the
deviation of each measurement from the average
A)
C)
B)
D)
* Highly precise measurement do not necessarily
guarantee accurate results.
Example 1
Average value
Student A
Student B
Student C
1.964 g
1.972 g
2.000 g
1.978 g
1.968 g
2.002 g
1.971 g
1.970 g
2.001 g
True value: 2.000 g
Therefore:
 Student C’s result is the most accurate and precise

EXERCISE
Three workers measure the mass of a 10.000 g mass on
several different kitchen balances.
worker A : 10.022 g, 9.976 g, 10.008 g
Worker B : 9.836 g, 10.033 g, 9.732 g
worker C : 10.230 g, 10.231 g, 10.232 g
Q1:Which set of data has the best precision?
Q2:Which has the best accuracy?
SCIENTIFIC NOTATION
 Very large and very small numbers can be simplified
written using a power of 10
 scientific notation
N x 10n
N = number between 1 – 10
n = exponent (+ve/–ve integer)
 The power of 10 is equal to the number of
places that the decimal point has been
moved:
 Moved to the left
+ve number
 67890
= 6.7890 x 104
 50000000= 5.0 x 107
 Moved to the right
-ve number
 0.0000312
= 3.12 x 10-5
 0.0468 = 4.68 x 10-2
Example 1:
Express the following in scientific notation
i) 4534.12
ii) 0.000000721
iii) 74.6
iv) 0.00203
v) 10026
SIGNIFICANT FIGURES
 The significant figures of a number are those digit
that carry meaning contributing to its precision
 Also known as significant digits.
 Each recorded measurement has a certain number
of significant digits.
 Calculations done on these measurements must
follow the rules for significant digits.
Guideline for using significant figures:
1. Any digit that is not zero is significant.
e.g: 1.234 kg  4 significant figures
2. Zeros between nonzero digits are significant
e.g: 606 m  3 significant figures
3. Zeros to the left of the first nonzero digit is not
significant
e.g: 0.0000349  3 significant figures
4. Number that is greater than 1, all the zeros written
to the right of the decimal point count as significant.
e.g: 2.0
 2 significant figures
50.054  5 significant figures
Number that is less than 1, only the zeros that are
at the end of the number and the zeros that are
between nonzero digits are significant.
e.g: 0.0220 
3 significant figures
0.5004 
4 significant figures
5. Number that do not contain decimal points, the
trailing zeros (zeros after the last nonzero digit) may
or may not be significant
 USE SCIENTIFIC NOTATION
e.g: 400
4 x 102 (1 s.f.)
or 4.0 x 102 (2 s.f.)
or 4.00 x 102 (3 s.f.)
0.004004500
Handling significant figures in calculation
 Addition and subtraction
The answer should have the same number of decimal
places as the quantity with the fewest number of
decimal places.
 Multiplication and division
The number of significant figures in the answer should
not be greater than the number of significant figures in
the least precise measurement
Example
Q1: 125.17 + 129 + 52.2 = ?
Solution:
1
2
5
1
2
9
5
2
.
1
.
2
7
.
Q2: 132.56 – 14.1 = ?
Solution:
1
3
2
.
5
1
4
.
1
.
6
Q3: 8.16 X 5.1355 = ?
Q3: 190.6 X 2.3 = ?
Example
Q: 8.16 m X 5.1355 m = ?
SOLUTION
3 s.f
5 s.f
(digit remains the same)
8.16 X 5.1355 = 41.9 0568
Drop digits
Fewest significant
figures (3 s.f)
41.9 m2
Q: 190.6 m X 2.3 m = ?
SOLUTION
(round off to 4)
(190.6) (2.3) = 43 8.38
440 m2
2 s.f
Drop digits
Fewest
significant
figures (2 s.f)
4.4 X 102 m2
Exercise
1) 0.225m x 0.0035m x (2.16 x 10-2 m)
2)
32.44 m + 4.9m – 0.304 m
82.94 m
3) Calculate the average of the two measured lengths 6.64
cm and 6.68 cm.
* Exact numbers are considered to have an infinite
number of significant figures.
 exact numbers could be obtained from definitions or
by counting numbers of objects.
 E.g :

500 sheets of paper in one ream

1m = 100cm
 There are exactly 100cm in one meter.
 Therefore, if a number is exact, it DOES NOT affect
the accuracy of a calculation nor the precision of the
expression
4)
1g
(4.80 x 104 mg)
1000 mg
11 55 cm3