default tick formatter could switch to scientific notation earlier

[anntzer]

Bug report

Bug summary

The default tick formatter switches to scientific notation only for very small values, but there is a range of slightly bigger values where scientific notation would be better too.

Code for reproduction

import matplotlib.pyplot as plt
plt.rcdefaults()
axs = plt.figure().subplots(2)
axs[0].set(xlim=(1e-7, 21e-7))
axs[1].set(xlim=(1e-8, 21e-8))
plt.show()

Actual outcome

Expected outcome

Either the top axes should also use scientific notation (note that this also happens e.g. 1e-6 and 1e-5), or we need something smarter to determine the number of ticks.
IIRC the default ticker places ticks assuming that labels will have a width of no more than ~3 character heights(?), so allowing for 4-5 digits before switching to scientific notation may make sense.

Matplotlib version

• Operating system: linux
• Matplotlib version: head, at least as far back as 3.0
• Matplotlib backend (print(matplotlib.get_backend())): qt5agg
• Python version: 37
• Jupyter version (if applicable):
• Other libraries:

[jklymak]

That’s my recollection. Ticks are spaced 3*fontsize apart.

[timhoffm]

That's controlled by the rcParam axes.formatter.limits = -7, 7.

Note that the %g notation already writes 1e-5. On that basis, I'd be fine with switching to -5, 5. Probably, nobody wants to read more than four digits anyway. 0.0003 is just fine, but you really start counting with 0.00003.