Geoscience Reference
In-Depth Information
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EXAMPLE 2.18
Problem:
How many significant figures are in 27,000.0?
Solution:
There are six significant figures: 2, 7, 0, 0, 0, 0. In this case, the .0 in 27,000.0 means that
the measurement is precise to 1/10 unit. The zeros indicate measured values and are not used solely
to place the decimal point.
2.6 POWERS AND EXPONENTS
In working with powers and exponents, the following key points are important:
•
Powers
are used to identify
area
, as in square feet, and
volume
, as in cubic feet.
• Powers can also be used to indicate that a number should be squared, cubed, etc. This later
designation is the number of times a number must be multiplied times itself.
• If all of the factors are alike, as 4 × 4 × 4 × 4 = 256, the product is called a
power
. Thus,
256 is a power of 4, and 4 is the
base
of the power. A power is a
product
obtained by using
a base a certain number of times as a factor.
• Instead of writing 4 × 4 × 4 × 4, it is more convenient to use an
exponent
to indicate that
the factor 4 is used as a factor four times. This exponent, a small number placed above and
to the right of the base number, indicates how many times the base is to be used as a factor.
Using this system of notation, the multiplication 4 × 4 × 4 × 4 is written as 4
4
. The
4
is the
exponent, showing that 4 is to be used as a factor 4 times.
• These same consideration apply to letters (
a
,
b
,
x
,
y
,
etc.) as well; for example:
z
2
=
z
×
z
z
4
=
z
×
z
×
z
×
z
Note:
When a number or letter does not have an exponent, it is considered to have an exponent of
one.
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EXAMPLE 2.19
Problem:
How is the term 2
3
written in expanded form?
Solution:
The power (exponent) of 3 means that the base number (2) is multiplied by itself three
times:
2
3
= 2 × 2 × 2
POWERS OF 1
POWERS OF 10
1
0
= 1
10
0
= 1
1
1
= 1
10
1
= 10
1
2
= 1
10
2
= 100
1
3
= 1
10
3
= 1000
1
4
= 1
10
4
= 10,000
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