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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 = 1e-06 = one millionths 10-9 = 1e-09 = one billionths 10-12 = 1e-12 = one trillionth 10-15 = 1e-15 = 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