Getting order of magnitude in Mathematica

Question

Is there a way to obtain the order of magnitude of a number in Mathematica? E.g. 200 would have an order of magnitude of 2.

score 6 · Accepted Answer · answered Apr 20 '11 at 19:31

6

You're looking for RealExponent. Strictly speaking, though, this is just as easily accomplished by Floor@Log[10, Abs[num]].

answered Apr 20 '11 at 19:31

rcollyer

IntegerExponent doesn't give the order of magnitude. Try `IntegerExponent[2300]`. – kennytm Apr 20 '11 at 19:33
@wrongusername On the page guide/Syntax in the documentation center, you'll find a few more of these useful abbreviations, look under the 'Short forms' header. At first they tend to be confusing, but you'll discover they come in handy once you start doing _functional programming_ stuff (see guide/FunctionalProgramming). – Sjoerd C. de Vries Apr 20 '11 at 22:09

score 4 · Answer 2 · answered Apr 20 '11 at 19:31

4

Start with

Log[10., 200]

2.30103

and use Round, Floor, Ceiling (or not) to taste.

answered Apr 20 '11 at 19:31

Bobby Treat

score 2 · Answer 3 · answered Apr 20 '11 at 19:29

2

Use IntegerLength to get the number of digits of an integer.

In[3]:= n=200;

In[4]:= IntegerLength[n] - 1

Out[4]= 2

Alternatively, if the number can be a non-integer, you could just use the log function

In[6]:= Floor[Log10[n]]

Out[6]= 2

answered Apr 20 '11 at 19:29

kennytm

nit, `n` can be negative which means `Log10` will return a complex number. – rcollyer Apr 20 '11 at 19:39

3 Answers3