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This module is from Elementary Algebra by Denny Burzynski and Wade Ellis, Jr. The basic operations with real numbers are presented in this chapter. The concept of absolute value is discussed both geometrically and symbolically. The geometric presentation offers a visual understanding of the meaning of |x|. The symbolic presentation includes a literal explanation of how to use the definition. Negative exponents are developed, using reciprocals and the rules of exponents the student has already learned. Scientific notation is also included, using unique and real-life examples.This module contains the exercise supplement for the chapter "Basic Operations with Real Numbers".

Exercise supplement

Signed numbers ( [link] )

For the following problems, find a if a is

Absolute value ( [link] )

Simplify the following problems.

Addition of signed numbers ( [link] ) - multiplication and division of signed numbers ( [link] )

Simplify the following problems.

( 2 ) ( 4 ) + 10 5

18 5

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3 ( 8 + 4 ) 12 4 ( 3 + 6 ) 2 ( 8 )

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1 ( 3 2 ) 4 ( 4 ) 13 + 10

7

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0 6 ( 4 ) ( 2 )

48

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Multiplication and division of signed numbers ( [link] )

Find the value of each expression for the following problems.

P = R C . Find P if R = 3000 and C = 3800 .

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z = x u s . Find z if x = 22 , u = 30 , and s = 8 .

1

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P = n ( n 1 ) ( n 2 ) . Find P if n = 3 .

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Negative exponents ( [link] )

Write the expressions for the following problems using only positive exponents.

a 3 b 2 c 5

a 3 b 2 c 5

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x 3 y 2 ( x 3 ) 7

x 3 y 2 ( x 3 ) 7

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4 2 a 3 b 4 c 5

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( 2 x + 9 ) 3 7 x 4 y 5 z 2 ( 3 x 1 ) 2 ( 2 x + 5 ) 1

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7 x y 3 z 2

7 x y 3 z 2

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3 2 a 5 b 9 c 2 x 2 y 4 z 1

c 2 y 4 z 9 a 5 b 9 x 2

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( z 6 ) 2 ( z + 6 ) 4

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16 a 5 b 2 2 a 3 b 5

8 a 2 b 3

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44 x 3 y 6 z 8 11 x 2 y 7 z 8

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( a 2 b ) 3

1 a 6 b 3

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( x 3 y 4 z 2 ) 6

y 24 z 12 x 18

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( x 6 y 2 ) 5

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( 2 b 7 c 8 d 4 x 2 y 3 z ) 4

b 28 c 32 y 12 z 4 16 d 16 x 8

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Scientific notation ( [link] )

Write the following problems using scientific notation.

0.000000000000537

5.37 × 10 13

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Convert the following problems from scientific form to standard form.

6.009 × 10 7

60 , 090 , 000

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3.88 × 10 5

0.0000388

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8.002 × 10 12

0.000000000008002

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2.101 × 10 15

2 , 101 , 000 , 000 , 000 , 000

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1 × 10 9

1 , 000 , 000 , 000

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Find the product for the following problems. Write the result in scientific notation.

( 1 × 10 5 ) ( 2 × 10 3 )

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( 3 × 10 6 ) ( 7 × 10 7 )

2.1 × 10 14

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( 2 × 10 14 ) ( 8 × 10 19 )

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( 9 × 10 2 ) ( 3 × 10 75 )

2.7 × 10 78

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( 1 × 10 4 ) ( 1 × 10 5 )

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( 8 × 10 3 ) ( 3 × 10 6 )

2.4 × 10 8

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( 9 × 10 5 ) ( 2 × 10 1 )

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( 3 × 10 2 ) ( 7 × 10 2 )

2.1 × 10 1

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( 7.3 × 10 4 ) ( 2.1 × 10 8 )

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( 1.06 × 10 16 ) ( 2.815 × 10 12 )

2.9839 × 10 28

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( 9.3806 × 10 52 ) ( 1.009 × 10 31 )

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Source:  OpenStax, Elementary algebra. OpenStax CNX. May 08, 2009 Download for free at http://cnx.org/content/col10614/1.3
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