Astronomy 105

Significant Figures

2. Significant figures
   

   When working out astronomical equations, you will be multiplying and dividing numbers and coming up with a final result (basic arithmetic). In most cases you will be using a calculator which displays results out to ten or more digits (or figures). However, not all of these digits are important or significant to the result. A good rule of thumb is:
   

   The precision of a final result can be no greater than the least precise factor that went into the equation.

   Here is an example. Say you are interested in determing how long it takes for light to travel from the Sun to the Earth. You look up the relevant quantities and plug them into the appropriate formula (see ).
   

   
   

   This number is what my calculator gives, but it has more digits than are really significant. Go back to the rule above. The two input factors are d = 1.496 X 10¹¹ m and v = 2.997925 10⁸ m/s. The first factor d has a precision of four digits (four significant figures) and the second factor v a precision of seven digits. Hence d is the less precise factor. The result is therefore only good to four digits and should have been expressed as t = 499.0 s. All of the other numbers are insignificant and should not be included in the answer. (Note that a zero after a decimal point is considered a significant figure.)