Logarithms and significant figures

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a.s.h.
Posts: 105
Joined: Tue Jan 28, 2014 3:50 pm

Logarithms and significant figures

Postby a.s.h. » Sat Mar 08, 2014 9:04 pm

Hi everyone,

How many significant figures should be reported when taking the log (base 10) of a number? For example, how would the value of log10 0.150 be reported with correct significant figures? (log10 0.150 ≈ -0.82391)

Also, does the rule for significant figures for base 10 logarithms apply for base e?
Thanks in advance.

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joe
Posts: 745
Joined: Fri Aug 29, 2003 11:57 am
Location: Sydney

Re: Logarithms and significant figures

Postby joe » Wed Mar 19, 2014 9:37 am

The number before the decimal point in a log gives the order of magnitude: it tells you the exponent of the original value. So, in this case only, count the digits after the decimal point as significant figures.
So log 0.150 ≈ -0.824
But log 0.000150 ≈ -3.824

For natural logs, this rule doesn't work. In that case, it is better to take the log of a value increased by one error and use that to estimate the errors.

Joe


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