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 :
The Sun's mass in grams is written :
,which is also written with 2 followed by 33 zeros.
The mass of a hydrogen atom in grams is written :
, 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 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 x : it is sufficient to add exponents to find , which is one million.
Logarithms are very useful for the planet researcher who juggles billions of stars and the thousandths of arcseconds.