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I've just heard about these terms. Could someone elaborate on what's their use is? And plus could you explain it using a few examples?

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    $\begingroup$ No one has used those terms in 40 years. $\endgroup$ – Gerry Myerson Jun 20 '16 at 7:29
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''Mantissa'' is a latin word which means '' something that is added ''. In the context of logarithms it indicate the decimal part of the logarithm of a number, while the ''characteristic'' is the integer part.

When I was young there were not home computers ( it seems incredible ?) and the logarithms was calculated using little books called ''logarithm tables''. In such books there was tabulated the mantissas, with some approximation, corresponding to a sequence of digits as:

Number $135$ : $\rightarrow$ mantissa $130334$

So, using the properties of the logarithms we was able to express the $log_{10}$ of all the numbers with these digits, simply counting the digits of the entire part of the given number :

$\log_{10}135=2.130334$

$\log_{10}13.5=1.130334$

$\log_{10}1350=3.130334$

Can you see what is the rule here? And where comes from?

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  • $\begingroup$ No. Could you explain? $\endgroup$ – Zlatan Jun 20 '16 at 7:19
  • $\begingroup$ $log_{10}1350=log_{10}(10^3\cdot 1.35)=log_{10} 10^3 + log_{10}1.35=3+0.130334$ $\endgroup$ – Emilio Novati Jun 20 '16 at 7:27
  • $\begingroup$ Great I get it thanks brother $\endgroup$ – Zlatan Jun 20 '16 at 7:30

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