College Algebra 9th txtbk

SECTION R–2 Exponents and Radicals 13
(C) 4y 3 (4y) 3 4y 3 (4) 3 y 3
4y 3 64y 3 60y 3 4y 3 (64)y 3
(D)
(2a 3 b 2 ) 2 2 2 a 6 b 4 a6
4b 4
MATCHED PROBLEM 2
Simplify using exponent properties, and express answers using positive exponents only.
9y 7
(A) (5x 3 )(3x 4 ) (B) (C) 2x 4 (2x) 4 (D)
6y 4
Z Scientific Notation
(3x 4 y 3 ) 2
Scientific work often involves the use of very large numbers or very small numbers. For
example, the average cell contains about 200,000,000,000,000 molecules, and the diameter
of an electron is about 0.000 000 000 0004 centimeter. It is generally troublesome to write
and work with numbers of this type in standard decimal form. The two numbers written
here cannot even be entered into most calculators as they are written. However, each can
be expressed as the product of a number between 1 and 10 and an integer power of 10:
200,000,000,000,000 2 10 14
0.000 000 000 0004 4 10 13
In fact, any positive number written in decimal form can be expressed in scientific notation,
that is, in the form
a 10 n
1 a 6 10, n an integer, a in decimal form
EXAMPLE 3 Scientific Notation
(A) Write each number in scientific notation: 6,430; 5,350,000; 0.08; 0.000 32
(B) Write in standard decimal form: 2.7 10 2 ; 9.15 10 4 ; 5 10 3 ; 8.4 10 5
SOLUTIONS
(A) 6,430 6.43 10 3 ; 5,350,000 5.35 10 6 ; 0.08 8 10 2 ;
0.000 32 3.2 10 4
(B) 270; 91,500; 0.005; 0.000 084
MATCHED PROBLEM 3
(A) Write each number in scientific notation: 23,000; 345,000,000; 0.0031; 0.000 000 683
(B) Write in standard decimal form: 4 10 3 ; 5.3 10 5 ; 2.53 10 2 ; 7.42 10 6
Most calculators express very large and very small numbers in scientific notation. Consult
the manual for your calculator to see how numbers in scientific notation are entered in
your calculator. Some common methods for displaying scientific notation on a calculator
are shown here.
Typical Scientific Typical Graphing
Number Represented Calculator Display Calculator Display
5.427 493 10 17 5.427493 – 17 5.427493E – 17
2.359 779 10 12 2.359779 12
2.359779E12