Scientific Notation
from Nearing Zero, http://www.nearingzero.net/science.html |

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 = 10^{3}, 100 = 10^{2}, 10 = 10^{1},
1 = 10^{0}, and 0.1 = 10^{-1}, the pattern is

3 X 10^{3} + 5 X 10^{2} + 2 X 10^{1} + 1 X 10^{0} + 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 10^{0} , since 10^{0} = 1.

Or, we could write it as

352.14 X 10^{1 }or 35.214 X 10^{2 }or 3.5214 X 10^{3}. 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 10^{3}, 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 10^{2};
4.7293 X 10^{3}; 4.7293 X 10^{4}; 4.7293 X 10^{5}; 4.7293 X 10^{6}

2. 925.38 = 9.2538 X 10^{2};
9.2538 X 10^{3}; 9.2538 X 10^{4};
9.2538 X 10^{5}; 9.2538 X 10^{6}

3. 8270913 = 8.270913 X 10^{2};
8.270913 X 10^{3}; 8.270913 X 10^{4};
8.270913 X 10^{5}; 8.270913 X 10^{6}

4. 4823873.563 = 4.82 X 10^{2};
4.82 X 10^{3}; 4.82 X 10^{4};
4.82 X 10^{5}; 4.82 X 10^{6}

5. 0.023 = 2.3 X 10^{0};
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 10^{0};
4.28 X 10^{-1}; 4.28 X 10^{-2};
4.28 X 10^{-3}; 4.28 X 10^{-4}

7. 2.34 x 10^{11} is

8. 5.63 x 10^{-5} is

a. -5.635

b. 563000

c. 0.0563

d. 0.0000563

e. 0.000563