Transcript Objective - To solve problems involving scientific notation

Objective - To use scientific notation to
write very large or very small numbers.
Scientific Notation
b
a  10
where 1  a  10
and b is any integer.
Examples:
9
6,320,000,000 = 6.32  10
9 jumps left
0.000027 = 2.7  10
5 jumps right
5
Large Numbers
59,000,000 = 5.9  10
7
7 jumps left
140,000,000,000 = 1.4  10
11
11 jumps left
Small Numbers
0.000426 = 4.26  10
4 jumps right
0.000009 = 9  10
6 jumps right
6
4
Write using scientific notation.
1) 81,000
4) 0.00015
4 jumps right
4 jumps left
8.1 10
1.5  10
4
2) 1,396,000
4
5) 0.0000317
6 jumps left
5 jumps right
1.396  10
6
3) 80,000,000,000
10 jumps left
8  10
10
3.17  10
6) 0.0000003
7 jumps right
3  10
7
5
Write each number in standard form.
5
1) 1.9  10
4) 3.41 106
1.90000
0000003.41
190,000
7
2) 2.43  10
00000002.43
0.000000243
9
3) 5.28  10
5.280000000
5,280,000,000
0.00000341
5) 6  10
600000000
600,000,000
8
6
6) 7  10
0000007
0.000007
Scientific Calculators
Enter:
3.6
900,000  4,000,000
12
means
3.6  10
12
or
3,600,000,000,000
Multiply using a scientific calculator
and write answer in scientific notation.
1) 2000  80,000
1.6  10
8
2) 4,000,000  5,000
2  10
10
3) 62,000  4,900,000
3.038  10
11
Multiplying with Scientific Notation
Multiply.
(2.110 )(1.5 10 )
8
6
2.1 10  1.5  10
8
6
(2.1)(1.5)  (10 )(10 )
8
3.15  10
8 6
3.15  10
14
6
Multiplying with Scientific Notation
Multiply.
(5.63 10 )(3.4 10 )
7
8
(5.63)(3.4)  (10 )(10 )
7
19.142  10
8
78
19.142  10
15
smaller
1.9142  10
16
larger
Not in
Scientific
Notation
Multiply.
14
11
1) (8 10 )(1.2 10 )
9.6 10
3) (3.7 10 )(6.5 10 )
10
8
24.05 1018
25
larger
smaller
2.405 1019
6
5
2) (2.4 10 )(4.9 10 ) 4)(9.7 10 )(8.6 10 )
7
9
11.76  10
16
smaller
larger
83.42 10
11
smaller
1.176  10
17
8.342 10
10
larger
Comparing Numbers in Scientific Notation
Order the following from greatest to least.
3.4 10
5
4.3 10
4
7.09 10
3.4 10
5
 0.000034 middle
4.3 10
4
 0.00043
7.09 10
6
largest
 0.00000709 smallest
4
5
4.3 10 , 3.4 10 , 7.09 10
6
6