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exponential notation

In physics, very large and very small numbers are written with the help of powers of the number ten. For large numbers, 10n with n a positive integer is a 1 with n trailing zeros:

100 = 1 = Eins
101 = 10 = ten
102 = 100 = a hundred
103 = 1000 = a thousand
106 = 1000000 = a million
109 = 1000000000 = a billion
1012 = 1000000000000 = a trillion
1015 = 1000000000000000 = a quadrillion

Very small fractions - numbers that differ very little from zero - can be written with the help of 10-n, with n a positive integer (n is, again, the number of zeros):

100 = 1 = one
10-1 = 0.1 = one tenth
10-2 = 0.01 = one hundredth
10-3 = 0.001 = one thousandth
10-6 = 0.000001 = one millionths
10-9 = 0.000000001 = one billionths
10-12 = 0.000000000001 = one trillionth
10-15 = 0.000000000000001 = one quadrillionth

 

Numbers that are not powers of ten can be written by factoring out the appropriate powers of ten. For instance,

1748 = 1.748·1000 = 1,748·103,

often written in what is called "scientific notation" as 1.748E3. On the other hand,

0.00041755 = 4.1755·10-4 = 4.1755E-4.


Variants

  • scientific notation
  • powers of ten