Order of magnitude Scientific notation

scientific notation enables simpler order-of-magnitude comparisons. proton s mass 6973167260000000000♠0.0000000000000000000000000016726 kg. if written 6973167260000000000♠1.6726×10 kg, easier compare mass of electron, given below. order of magnitude of ratio of masses can obtained comparing exponents instead of more error-prone task of counting leading zeros. in case, −27 larger −31 , therefore proton 4 orders of magnitude (7004100000000000000♠10,000 times) more massive electron.

scientific notation avoids misunderstandings due regional differences in quantifiers, such billion, might indicate either 10 or 10.

in physics , astrophysics, number of orders of magnitude between 2 numbers referred dex , contraction of decimal exponent . instance, if 2 numbers within 1 dex of each other, ratio of larger smaller number less 10. fractional values can used, if within 0.5 dex, ratio less 10, , on.