I am edit answer with @DanielF explanation: "floor doesn't convert to integer, it just gives integer-valued floats, so you still need an astype to change to int" Check this code to understand the solution:

import numpy as np
arr = np.random.rand(1, 10) * 10
print(arr)
arr = np.floor(arr).astype(int)
print(arr)

OUTPUT:
[[2.76753828 8.84095843 2.5537759  5.65017407 7.77493733 6.47403036
  7.72582766 5.03525625 9.75819442 9.10578944]]
[[2 8 2 5 7 6 7 5 9 9]]

Neither Python built-in nor numpy's version of ceil/floor support precision.

One hint though is to reuse round instead of multiplication + division (should be much faster):

def my_ceil(a, precision=0):
    return np.round(a + 0.5 * 10**(-precision), precision)

def my_floor(a, precision=0):
    return np.round(a - 0.5 * 10**(-precision), precision)

UPD: As pointed out by @aschipfl, for whole values np.round will round to the nearest even, which will lead to unexpected results, e.g. my_ceil(11) will return 12. Here is an updated solution, free of this problem:

def my_ceil(a, precision=0):
    return np.true_divide(np.ceil(a * 10**precision), 10**precision)

def my_floor(a, precision=0):
    return np.true_divide(np.floor(a * 10**precision), 10**precision)