Geology Reference
In-Depth Information
Exercise 3 • Measurements, Basic Calculations and Conversions, and Graphs
37
Scientific Notation
Often numbers in science are very large or very small.
Scientists have devised scientific notation as a way of
saving space, minimizing the chance of dropping a
zero or two, and speeding calculations and communi-
cations. The technique employs the exponent (in this
case the power of 10), which is tacked on to a 10 (i.e.,
10
3
or 10
X
10
X
10 or 1000 are equal; the "3" is the
exponent), and is multiplied by another number (usu-
ally between 0.1 and 10) to indicate the size of the
number. If it is a positive exponent it means we need to
increase the number in front of the 10 by the number of
zeros equal to the exponent. If it is a negative number,
it means we decrease the number by the number of
zeros equivalent to the exponent. For example,
4X 10
3
actually means 4
X
10
X
10
X
10 = 4
X
1000
= 4,000. 2.3
X
10
9
actually means 2.3
X
1,000,000,000,
or, when we move the decimal point nine spaces to the
right in 2.3, the number is 2,300,000,000 and would be
said as two billion 300 million, or more easily as 2.3 bil-
lion. In fact when we see 2.3
X
10
9
, in most cases we
say 2.3 billion.
We also use this system for small numbers.
2.3
X
10"
3
actually means that we move the decimal
point over three spaces to the left; the number is 0.0023.
We also put a zero to the left of the decimal point to
emphasize the decimal. Another advantage of scien-
tific notation is in recognition of significant figures
(described below).
Another option is to use prefixes to describe very
large and very small numbers. We often deal in mil-
lions and billions of years in the geosciences. We use
the terms million and billion, but we also use the term
mega for million and giga for billion, as in megawatts
and gigayears. Actually, the French word annee is
used for year in SI; it is abbreviated as (a), but some
geologists still use the word year (yr).
The full ranges of these prefixes are in Appendix
I. They range from 10
18
, which is known as exa- (E is
the symbol) for 1,000,000,000,000,000,000 (a quintillion,
which has 18 zeros after the 1) to 10~
18
, which is known
as atto (a is the symbol) for a very small quantity, that
is, 0.000,000,000,000,000,001. Spaces, not commas, are
used in the SI system between the sets of zeros. Com-
mas have been included here for ease of reading.
number, the number of significant figures is the num-
ber of digits from the first nonzero digit on the left to
the last digit (zero or nonzero) on the right. For exam-
ple, 22,000.0 has six significant figures. Other exam-
ples of significant figures are 0.0022 has two significant
figures, 2.2
X
10
3
has two significant figures, and
2.20
X
10
3
has three significant figures. The last two
examples show the use of scientific notation in deter-
mining significant digits. It is important to note that
when two numbers (or more) are multiplied or
divided, the number of significant figures of the new
number is the value of the smallest number of signifi-
cant figures of the numbers multiplied or divided. For
instance, if 17.0 is divided by 7.00, the answer is
reported as 2.42 (three significant figures). If 17.0 is
divided by 7.0, the number is reported as 2.4 (two sig-
nificant figures, as 7.0 has only two significant figures).
In neither example is the answer reported as
2.428571429, which is the result you may see if you use
a calculator. Reporting that number as your answer
would indicate 10 significant figures, when, in fact,
there were only two or three significant figures
(depending on example above).
QUESTIONS 3, PART A
1.
What is the SI unit for measuring:
a.
distance?
b.
temperature?
2.
Why might geoscientists not use SI Units in working with
some maps produced in the United States?
3.
Give the value in words and numbers for the following
numbers, which are given in scientific notation (the first is
given for you).
Scientific
Notation
Numbers
Words
one million two
hundred thousand
(or 1.2 million)
1,200,000
a. 1.2
x
10
6
Significant Figures
Significant figures provide an indication of the preci-
sion with which a quantity is known. The more precise
a number is, the more significant figures it has. For
example, the number 2.43 has three significant figures.
The actual value of this number may be between 2.425
and 2.435. If there is no decimal point in a number, the
number of significant figures is the number of digits
from the first nonzero digit on the left to the last
nonzero digit on the right. For example, 22,000 has two
significant figures. If there is a decimal point in the
b. 4.12
x
10
3
c. 5.8
x
10
9
d. 2.2
x
10
1
5
e. 0.1
x
10
6
