import matplotlib.pyplot as plt

fig, ax = plt.subplots()
ax.set(title="Two y-scales", ylabel="x / m")
# right ax:
axr = ax.twinx()
axr.set_ylabel("x / cm")


def track_yax(ax_):
    """Syncronize second y-axis with first axis. """
    y1, y2 = ax.get_ylim()
    axr.set_ylim(100*y1, y2*100)
    # axr.figure.canvas.draw() # does not make a difference
    yr1, yr2 = axr.get_ylim()
    print(f"Lower: {y1:+.5g} -> {yr1:+.5g}\t Upper: {y2:+.5g} -> {yr2:+.5g}")


# automatically update ylim of ax2 when ylim of ax1 changes.
ax.callbacks.connect("ylim_changed", track_yax)


# Do the plotting:
ax.plot([0, 5, 2, 4, 1], 'o-')
ax.grid(True)

plt.show()