Scientific Notation - Order of Magnitude

Order of Magnitude

Scientific notation also enables simpler order-of-magnitude comparisons. A proton's mass is 0.0000000000000000000000000016726 kg. If written as 1.6726×10−27 kg, it is easier to compare this mass with that of an electron, given below. The order of magnitude of the ratio of the masses can be obtained by comparing the exponents instead of the more error-prone task of counting the leading zeros. In this case, −27 is larger than −31 and therefore the proton is roughly four orders of magnitude (about 10000 times) more massive than the electron.

Scientific notation also avoids misunderstandings due to regional differences in certain quantifiers, such as billion, which might indicate either 109 or 1012.

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