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Scientific Notation
Scientific Notation
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A method of describing very large numbers as a product of two factors.
The first factor is greater than or equal to 1 and less than 10. The
second factor is a power of 10.
Example: 2.5 x 105
Power of 10
107
106
105
104
103
102
101
100
Standard Form
10 000 000
1 000 000
100 000
10 000
1000
100
10
1
Example 1:
Solar wind is released from the sun at speeds of about
1 450 000km/h. Write this number in scientific notation.
1) Rewrite the number as a product:
1 450 000 = 1.45 x 1 000 000
2) Rewrite the second factor as a power of ten:
1 450 000 = 1.45 x 1 000 000
= 1.45 x 106
Try it:
1) 2 345 000
2) 300
3) 45 000
4) 4500
5) 28 000 000
6) 208 000
Example 2:
The number of hair follicles on a human body is estimated at
5.0 x 106. Write 5.0 x 106 in standard form.
5.0 x 106 = 5.0 x 1 000 000
= 5 000 000
Try it:
1) 4.5 x 104
2) 7.6 x 103
3) 7.02 x 104
4) 8.4 x 106
5) 3.213 x 107
6) 4.5 x 102
Practice:
Write each number in scientific notation:
1) 47 740
2) 8 141 000
3) 541 000
4) 937 000 000
5) 5400
6) 326 000 000
7) 49 000
8) 28 000 000
9) 1 010 000 000
10) 604 000
11) 370 000
12) 531.4
13) 78.64
14) 64.38
15) 6.113
Convert from scientific notation to standard form:
1) 8.932 x 106
2) 9.43 x 103
3) 6.1 x 105
4) 7.2 x 107
5) 1.7 x 104
6) 1.08 x 108
7) 6.457 x 105
8) 8.9 x 105
9) 4.5 x 102
10) 5.67 x 101
11) 4.003 x 100
12) 3 x 1010