## Logarithms and significant figures

A forum designed mainly for high school physics students in New South Wales, Australia.
a.s.h.
Posts: 110
Joined: Tue Jan 28, 2014 3:50 pm

### Logarithms and significant figures

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?
joe
Posts: 755
Joined: Fri Aug 29, 2003 11:57 am
Location: Sydney

### Re: Logarithms and significant figures

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