Scientific notation is a convenient and concise way to express large and small numbers. Most numbers is astronomy are large so I will use large numbers for my examples. The basic idea (which I hope is review for all of you) is that a large number is expressed as a multiplier times a factor of ten.
For example, we can write 143,068 as 1.43068 X 105 or
4,280,000,000 as 4.28 X 109. What I did to convert
was take the significant digits (all digits except trailing zeros) and
express them as a number between one and ten: (1.43068; 4.28). This
becomes the factor. To get the exponent, I counted how far I had
to move the decimal point (implicitly at the end of an integer) to get
the factor:
Since I moved the decimal point five places, the exponent is 5, hence 143,068 = 1.43068 X 105. Check that the other conversion was done correctly.
To use scientific notation in your calculator, you would enter the
factor first then press the exponent key
and the exponent. For example, to enter
1.43068 X 105 type
.
Your calculator display should now read something like
1.43068 05, which is a shorthand notation. Since every number in
scientific notation includes ``X 10,'' this factor is assumed but
not displayed on a calculator. On your paper, however, you must write
1.43068 X 105.
Most of the homework problems will involve scientific notation, so it is important to review this important notation.
Next: Significant Figures