Download B4E-Scientific Notation

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Date ————————————
BENCHMARK 4
(Chapters 7 and 8)
E. Scientific Notation
(pp. 74–75)
Any real number can be written in standard form or in scientific notation. A number
written in scientific notation is in the form c 3 10n, where c is greater than or equal to
1 and less than 10, and n is an integer. For example, the number two million can be
written in standard form as 2,000,000, or in scientific notation as 2 3 106. The number
five thousandths can be written in standard form as 0.005, or in scientific notation as
5 3 1023.
1. Writing Numbers in Scientific Notation
EXAMPLE
Write each number in scientific notation.
a. 0.00000317
b. 8,356,000,000
Solution:
PRACTICE
b. Move the decimal point 9 places to
the right. The exponent is 26.
0.00000317 5 3.17 3 1026
the left. The exponent is 9.
8,356,000,000 5 8.356 3 109
Write each number in standard form.
a. 1.982 3 107
b. 8.04 3 1025
Solution:
a. The exponent is 7. Move the
b. The exponent is 25. Move the
decimal point 7 places to
the right.
1.982 3 107 5 19,820,000
decimal point 5 places to
the left.
8.04 3 1025 5 0.0000804
Write the number in scientific notation.
1. 42,635,000,000,000
2.
0.0000000000582
3. 73,009
Write the number in standard form.
BENCHMARK 4
E. Scientific Notation
4.
74
7.81 3 1012
5.
5.403 3 1028
6. 6.034 3 102
2. Computing with Scientific Notation
EXAMPLE
Evaluate the expression. Write the answer in scientific notation.
a. (4.3 3 105)(2.8 3 109)
Algebra 1
Benchmark 4 Chapters 7 and 8
b.
4.5 3 107
}
7.5 3 1024
c. (9.2 3 1026)4
Copyright © by McDougal Littell, a division of Houghton Mifflin Company.
EXAMPLE
For a positive
number written in
scientific notation,
c 10n:
if n < 0, the
number is
between 0 and 1,
if n r 0, the
number is
greater than 1.
a. Move the decimal point 6 places to
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Date ————————————
Benchmark 4
(Chapters 7 and 8)
Solution:
a. (4.3 3 105)(2.8 3 109)
5 (4.3 + 2.8) 3 (105 + 109)
Commutative property and
associative property
5 12.04 3 1014
Product of powers property
5 (1.204 3 101) 3 1014
Write 12.04 in scientific notation.
5 1.204 3 (101 3 1014)
Associative property
5 1.204 3 1015
Product of powers property
4.5 3 107
4.5
107
}
}
b. }
24 5 7.5 3
7.5 3 10
1024
Product rule for fractions
5 0.6 3 1011
Quotient of powers property
5 (6.0 3 1021) 3 1011
Write 0.6 in scientific notation.
5 6.0 3 (1021 3 1011)
Associative property
5 6.0 3 1010
Product of powers property
PRACTICE
Power of a product property
5 7163.9296 3 10224
Power of a power property
5 (7.1639296 3 103) 3 10224
Write in scientific notation.
5 7.1639296 3 (103 3 10224)
Associative property
5 7.1639296 3 10221
Product of powers property
Evaluate the expression. Write the answer in scientific notation.
7. (3.6 3 106)(8.14 3 105) 8.
5.6 3 107
10. }
7 3 1025
11.
(4.9 3 1015)3
1.5 3 1022
7.5 3 10
}
12
9. (6.02 3 1023)(3.1 3 102)
12. (2.6 3 1024)25
Quiz
If the number is in standard form, write it in scientific notation. If the
number is in scientific notation, write it in standard form.
1. 5.026 3 1028
2.
0.00002707
3. 618,090,300,000,000
4. 0.001001001001001
5.
3.11 3 1014
6. 9.45824 3 1023
Evaluate the expression. Write the answer in scientific notation.
7. (7.2 3 1026)(5.3 3 1010) 8.
10.
2.1 3 1015
2.4 3 10
}8
11.
(1.6 3 1012)2
2.56 3 10212
6.4 3 10
}
9
9. (3.14 3 1025)(8.2 3 103)
BENCHMARK 4
E. Scientific Notation
Copyright © by McDougal Littell, a division of Houghton Mifflin Company.
c. (9.2 3 1026)4 5 (9.2)4 3 (1026)4
12. (8.8 3 106)3
Algebra 1
Benchmark 4 Chapters 7 and 8
75
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