Astronomy
Scientific Notation
Objectives:
Convert a power of ten to a standard decimal number.
Convert a number expressed in scientific notation to standard decimal format.
Brief review of powers of ten:
103 means 10 X 10 X 10 = 1000
10-4 means
1
1
1


 0.0001
4
10
10  10  10  10 10000
107 is 10 000 000 (Note: Science uses spaces not commas for grouping)
10-7 is 0.000 000 1 (Note: Science also uses a 0 in front of the decimal)
Practice problems for powers of ten:
Express each power of ten as a standard number. Check your answers with the answers given below.
1) 102
2) 105
3) 108
4) 104
5) 10-1
6) 10-2
7) 10-6
8) 10-4
9) 109
10) 10-9
Answers to powers of ten problems:
1) 100
2) 100 000
5) 0.1
6) 0.01
9) 1 000 000 000
10) 0.000 000 001
3) 100 000 000
7) 0.000 001
4) 10 000
8) 0.000 1
Brief review of scientific notation:
7.23 X 103 means 7.23 X 1000 which is 7230. For a short cut, start with 7.23 and move the decimal three places right, ie,
7230.
1.8 X 105 means start with 1.8 and move the decimal five places right, ie, 180 000.
9.637 X 10-2 means 9.637 X 0.01 which is 0.09637. For a short cut, start with 9.637 and move the decimal two places left, ie,
0.0967.
2.5 X 10-6 means move the decimal six places to the left, ie, 0.000 002 5
Practice problems for scientific notation:
Express each number in standard form (without using scientific notation). Check your answers against the answers given
below.
1) 1.3 X 103
11) 9.3 X 105
2) 5.2 X 106
12) 7.2 X 10-2
3) 4.84 X 10-3
13) 5.9 X 10-6
4) 6.0 X 10-5
14) 6.25 X 10-4
5) 3.7 X 108
15) 8.91 X 10-5
6) 2 X 107
16) 3.2 X 101
7) 2 X 10-7
17) 5.7 X 108
8) 8.1 X 101
18) 4.2 X 100
9) 8.1 X 100
19) 1.2 X 1019 (miles to Andromeda Galaxy)
10 8.1 X 10-1
20) 9.1 X 10-31 (mass of an electron)
Answers to scientific notation problems:
1) 1300
2) 5 200 000
3) 0.00484
4) 0.000 06
5) 370 000 000
6) 20 000 000
7) 0.000 000 2
8) 81
9) 8.1
10) 0.81
11) 930 000
12) 0.072
13) 0.000 005 9
14) 0.000 625
15) 0.000 089 1 16) 32
17) 570 000 000
18) 4.2
19) 12 000 000 000 000 000 000
20) 0.000 000 000 000 000 000 000 000 000 000 91
More practice problems can be found on the web here:
http://janus.astro.umd.edu/astro/scinote/ or at
http://www.khanacademy.org/video/scientific-notation?playlist=ck12.org%20Algebra%201%20Examples