Compute with scientific notation
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Transcript of Compute with scientific notation
Algebra
8.4Scientific Notation
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
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
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
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
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
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.
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
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
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
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
Homework
pg. 63 #’s 1, 2, 4, 6, 8, 9, 10, 11