How can I print many significant figures in Python?

Question

For a scientific application I need to output very precise numbers, so I have to print 15 significant figures. There are already questions on this topic here, but they all concern with truncating the digits, not printing more.

I realized that the print function converts the input float to a 10 character string. Also, I became aware of the decimal module, but that does not suit my needs.

So the question is, how can I easily print a variable amount of signifcant figures of my floats, where I need to display more than 10?

Answer 1

Let:

>>> num = 0.0012345

For 3 significant figures:

>>> f'{num:.3}'
'0.00123'

For 3 decimal places:

>>> f'{num:.3f}'
'0.001'

See the "presentation types for floating point and decimal" table at the bottom of this section for any additional requirements provided by e, E, f, F, g, G, n, %, None.

Answer 2

You could use the string formatting operator %:

In [3]: val = 1./3

In [4]: print('%.15f' % val)
0.333333333333333

or str.format():

In [8]: print(str.format('{0:.15f}', val))
Out[8]: '0.333333333333333'

In new code, the latter is the preferred style, although the former is still widely used.

For more info, see the documentation.

Answer 3

Thought the original question wanted to format n significant figures, not n decimal points. So a custom function might be required until some more native built-in types are on offer? So you'll want something like:

def float_nsf(q,n):
    """
    Truncate a float to n significant figures.  May produce overflow in 
    very last decimal place when q < 1.  This can be removed by an extra 
    formatted print. 
    Arguments:
      q : a float
      n : desired number of significant figures
    Returns:
    Float with only n s.f. and trailing zeros, but with a possible small overflow.
    """
    sgn=np.sign(q)
    q=abs(q)
    n=int(np.log10(q/10.)) # Here you overwrite input n!
    if q<1. :
        val=q/(10**(n-1))
        return sgn*int(val)*10.**(n-1)
    else:
        val=q/(10**n)
        return sgn*int(val)*10.**n

Answer 4

To display N significant figures (not decimal places) you use the "g" format:

>>> x = 1.23
>>> print("%.2g" % x)
1.2
>>> x = 12.3
>>> print("%.2g" % x)
12

See format spec for details on precision:

The precision is a decimal number indicating how many digits should be displayed after the decimal point for a floating point value formatted with 'f' and 'F', or before and after the decimal point for a floating point value formatted with 'g' or 'G'. For non-number types the field indicates the maximum field size - in other words, how many characters will be used from the field content. The precision is not allowed for integer values.

Answer 5

Use these two common print idioms for formatting. Its a matter of personal taste on which is better.

value = 10/3            #gives a float of 3.33333.....

print '%.15f' % value
print str.format('{0:.15f}', value)

Personally I think the first is more compact and the 2nd is more explicit. Format has more features when working with multiple vals.

Answer 6

You could use this function I wrote, it seems to be working fine and it's quite simple!:

def nsf(num, n=1):
    """n-Significant Figures"""
    numstr = ("{0:.%ie}" % (n-1)).format(num)
    return float(numstr)

1. It first converts the number to a string using exponent notation
2. Then returns it as float.

Some tests:

>>> a = 2./3
>>> b = 1./3
>>> c = 3141592
>>> print(nsf(a))
0.7
>>> print(nsf(a, 3))
0.667
>>> print(nsf(-a, 3))
-0.667
>>> print(nsf(b, 4))
0.3333
>>> print(nsf(-b, 2))
-0.33
>>> print(nsf(c, 5))
3141600.0
>>> print(nsf(-c, 6))
-3141590.0

I hope this helps you ;)