How can I print many significant figures in Python?

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.

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.