| Scientific Notation Although we will keep things as simple as possible in this course, there are some concepts that you need to learn because of the very nature of astronomy and the vast size and mass scales it deals with. from Nearing Zero, http://www.nearingzero.net/science.html |
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Our number system is described as being base ten. This statement means that a number like
3521.4
means "3 times 1000 + 5 times 100 + 2 times 10 + 1 times 1 + 4 times 0.1."
If we use the fact that 1000 = 103, 100 = 102, 10 = 101, 1 = 100, and 0.1 = 10-1, the pattern is
3 X 103 + 5 X 102 + 2 X 101 + 1 X 100 + 4 X 10-1.
Thus, all the numbers are expressed in terms of powers of ten.
We can write this number as
3521.4 X 100 , since 100 = 1.
Or, we could write it as
352.14 X 101 or 35.214 X 102 or 3.5214 X 103. They are all identical in value, since they just involve pulling out one or more powers of ten and multiplying the whole number by this amount, and then reducing the number by the same number of powers of ten by shifting the decimal point the appropriate number of places to the left. These forms of our starting number show the nature of scientific notation. Since we often do not want to carry around too many digits, we can write approximately that
3521.4 = 3.52 X 103, and this example shows how we will use scientific notation in the course..
Try your understanding by clicking on the best answers:
1. 47293 = 4.7293 X 102; 4.7293 X 103; 4.7293 X 104; 4.7293 X 105; 4.7293 X 106
2. 925.38 = 9.2538 X 102; 9.2538 X 103; 9.2538 X 104; 9.2538 X 105; 9.2538 X 106
3. 8270913 = 8.270913 X 102; 8.270913 X 103; 8.270913 X 104; 8.270913 X 105; 8.270913 X 106
4. 4823873.563 = 4.82 X 102; 4.82 X 103; 4.82 X 104; 4.82 X 105; 4.82 X 106
5. 0.023 = 2.3 X 100; 2.3 X 10-1; 2.3 X 10-2; 2.3 X 10-3; 2.3 X 10-4
6. 0.000428 = 4.28 X 100; 4.28 X 10-1; 4.28 X 10-2; 4.28 X 10-3; 4.28 X 10-4
7. 2.34 x 1011 is
8. 5.63 x 10-5 is
a. -5.635
b. 563000
c. 0.0563
d. 0.0000563
e. 0.000563