Observatoire de Paris
<-   Notations   ->
  • decimal numbers : 2.5 is a better notation for 2,5

  • powers (or exponents) are useful to give huge quantities (the solar mass in grams for instance) or very small quantities (the mass of a hydrogen atom in grams).

    The positive exponent gives the number of zeros :

    The negative exponent also gives the number of zeros, but with a subtraction sign : 10^(-3)=0.001=1/1000

    The Sun's mass in grams is written : 2*10^33 ,which is also written with 2 followed by 33 zeros.

    The mass of a hydrogen atom in grams is written : 1.7*10^(-25) , which is also written with 25 zeros followed by 17, with a dot after the first zero.

  • logarithms : this is the function that gives the power of a number :

    The decimal logarithm or "log" of 10^33 is 33

    This replaces some multiplications with some additions (it is easier to do). It is more difficult to calculate 0.0001 x 10000000000 than it is to calculate 10^(-4) x 10^10 : it is sufficient to add exponents to find 10^6, which is one million.

    Logarithms are very useful for the planet researcher who juggles billions of stars and the thousandths of arcseconds. log (x y) = log(x) + log (y)