Transcript FS1003 Introduction to analysis

Introduction to analysis
Data handling, errors and so on
Common Decimal Prefixes Used with SI Units.
Prefix
tera
giga
mega
kilo
hecto
deka
----deci
centi
milli
micro
nano
pico
femto
Prefix
Symbol
Number
Word
Exponential
Notation
T
1,000,000,000,000
trillion
G
1,000,000,000
billion
M
1,000,000
million
k
1,000
thousand
h
100
hundred
da
10
ten
---1
one
d
0.1
tenth
c
0.01
hundredth
m
0.001
thousandth
millionth
n
0.000000001
billionth
p
0.000000000001
trillionth
f
0.000000000000001
quadrillionth
1012
109
106
103
102
101
100
10-1
10-2
10-3
10-6
10-9
10-12
10-15
Rules for Determining Which
Digits are Significant
All digits are significant, except zeros that are used only to
position the decimal point.
1. Make sure that the measured quantity has a decimal point.
2. Start at the left of the number and move right until you
reach the first nonzero digit.
3. Count that digit and every digit to its right as significant.
Zeros that end a number and lie either after or before the
decimal point are significant; thus 1.030 ml has four
significant figures, and 5300. L has four significant figures
also. Numbers such as 5300 L is assumed to only have 2
significant figures. A terminal decimal point is occasionally
used to clarify the situation, but scientific notation is the best!
Examples of Significant Digits in Numbers
Number
0.0050
18.00
0.0012
83.001
875,000
30,000
5.0000
23,001.00
0.000108
1,470,000
- Sig digits
two
four
two
five
three
one
five
seven
three
three
Number
-
1.3400 X 107
5600
87,000
78,002.3
Sig digits
five
two
two
six
0.00007800
four
1.089 X 10-6
0.0000003
1.00800
1,000,000
four
one
six
one
Rules for Significant Figures in Answers
1. For multiplication and division.
The number with the least certainty limits the certainty of the result.
Therefore, the answer contains the same number of significant
figures as there are in the measurement with the fewest significant
figures.
Multiply the following numbers:
9.2 cm x 6.8 cm x 0.3744 cm = 23.4225 cm3 = 23 cm3
2. For addition and subtraction.
The answer has the same number of decimal places as there are in the
measurement with the fewest decimal places.
Add the following volumes:
83.5 ml + 23.28 ml = 106.78 ml = 106.8 ml
Example subtracting two volumes:
865.9 ml - 2.8121393 ml = 863.0878607 ml = 863.1 ml
Rules for Rounding Off Numbers:
1. If the digit removed is 5 or more, the preceding number increases
by 1 : 5.379 rounds to 5.38 if three significant figures are retained and to
5.4 if two significant figures are retained.
2. If the digit removed is less than 5, the preceding number is
unchanged : 0.2413 rounds to 0.241 if three significant figures are
retained and to 0.24 if two significant figures are retained.
3. Be sure to carry two or more additional significant figures through a
multistep calculation and round off only the final answer.
Precision and Accuracy
Errors in Scientific Measurements
Precision - Refers to reproducibility or How close the
measurements are to each other.
Accuracy - Refers to how close a measurement is to the
real value.
Systematic error - produces values that are either all higher
or all lower than the actual value.
Random Error - in the absence of systematic error, produces
some values that are higher and some that
are lower than the actual value.
Constant & Proportional Errors
Constant errors
Proportional errors
9
8
7
6
5
4
3
2
1
0
10
8
6
4
2
0
0
1
2
3
4
5
6
7
0
1
2
3
4
5
6
7