Download - Compute with scientific notation
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Algebra
8.4Scientific Notation
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The Form
A number is written in scientific notation when it is in the form
where c is a value 1and<10
andnis aninteger.
nc×10
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The Form
7.65 10
where c is a value 1and<10
andnis aninteger.
nc×10
43.12 10
Not Scientific Notation Scientific Notation
331.2 1066.5 10
68042 10 38.042 10
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Large and small values
One purpose of scientific notation is to allow you to write very large numbers and very small numbers easily, without lots of 0’s.
48.4912×10
Small numbers have negative exponents.
84,912
Large numbers have positive exponents.
- 42.65×10.000265
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Scientific Notation Decimal
Move decimal point right for positive exponent.Move decimal point left for negative exponent.
33.128×101. 3128
46.4 ×102. 64,000
- 13.9×103.
- 56.12×104.
.39
.0000612
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Decimal Scientific Notation
Move decimal point right or left to arrange one digit to the left of decimal point.
45.2314 ×101. 52,314
03.2×102. 3.2
3.
4. 602,000,000
Move left 4 places
No need to move
.0000428 Move right 5 places- 54.28×10
Move left 8 places86.02×10
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Exercises
22.834 ×101. 283.4- 61.23×102. .00000123
43.469×103.
- 23.9×104.
34,690
.039
Rewrite in decimal form.
Rewrite in scientific notation.
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Computing with Scientific Notation
Another purpose of scientific notation is to allow you to compute with large and small values easily using the rules of exponents.
Numbers can be multiplied.
4 2
4 2
4+2 6 7
(8×10 )(3×10 )
=(8×3)(10 ×10 )
=24 ×10 =24 ×10 =2.4×10
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Computing with Scientific Notation
Numbers can be divided.
6 6
2 2
6-2 4
4.8×10 4.8 10= ×
2.4 ×10 2.4 10
=2×10 =2×10
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Exercise
Evaluate. Write answer in scientific notation.
4 3(1.4 ×10 )(7.6×10 )
4 3=(1.4 ×7.6)(10 ×10 ) Associative property
710.64 ×10 Simplify
81.064 ×10 Rewrite in SN
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Exercise
Evaluate. Write answer in scientific notation.- 3
- 5
(8×10 )(5×10 )
- 3
- 5
8 10=
5 10Associative property
- 3- (- 5)1.6×10 Subtract exponents
21.6×10 Simplify to SN
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Homework
pg. 63 #’s 1, 2, 4, 6, 8, 9, 10, 11